1 00:00:00,980 --> 00:00:01,580 OK. 2 00:00:01,610 --> 00:00:02,750 Hello again, everybody. 3 00:00:02,780 --> 00:00:07,310 So in this lecture, we are going to go over something called logic. 4 00:00:08,000 --> 00:00:15,680 You may have heard of this before depends on kind of what context you might have heard it in. 5 00:00:15,920 --> 00:00:22,370 But it definitely is something that applies to programming, but definitely more than just programming. 6 00:00:22,460 --> 00:00:25,010 Logic isn't necessarily just a programming thing. 7 00:00:25,460 --> 00:00:30,170 It can apply to philosophy and all kinds of stuff. 8 00:00:30,320 --> 00:00:36,320 You know, sometimes just general discussions between people can involve or not involve logic. 9 00:00:37,610 --> 00:00:40,750 So it's more than just programming, but very important for programming. 10 00:00:40,760 --> 00:00:41,990 So that's why we're going over it. 11 00:00:43,650 --> 00:00:46,110 So like I said, you most likely have heard of logic. 12 00:00:46,380 --> 00:00:51,600 Some of you might have referred to logic is something more akin to just using common sense. 13 00:00:52,200 --> 00:00:59,040 An example here is kind of a simple one, but you know, if all dogs have a keen sense of smell. 14 00:00:59,370 --> 00:01:04,490 And my pet is a dog, then my pet has a keen sense of smell. 15 00:01:04,500 --> 00:01:10,980 You can kind of just deduce that from these previous lines here, since all the dogs have a keen sense 16 00:01:10,980 --> 00:01:11,610 of smell. 17 00:01:12,130 --> 00:01:16,800 You know you have your pet as a dog, then you go back and you say, Well, this is a dog. 18 00:01:16,980 --> 00:01:22,290 I just now found out that they have a keen sense of smell, so that means that this one dog, that's 19 00:01:22,290 --> 00:01:25,080 my pet, must also have a keen sense of smell. 20 00:01:26,600 --> 00:01:30,270 Something that doesn't probably doesn't need explanation, you're probably like, why? 21 00:01:30,500 --> 00:01:31,700 Why do we care about this? 22 00:01:31,700 --> 00:01:32,590 This is obvious. 23 00:01:33,740 --> 00:01:36,710 Sometimes the logic can get a little more complex. 24 00:01:37,790 --> 00:01:40,850 This is an incredibly complex, but let's look at another example. 25 00:01:41,920 --> 00:01:47,080 If Bob doesn't not have a watermelon, he will not get all bananas. 26 00:01:47,110 --> 00:01:55,990 If both oranges and red or yellow apples are available, so this is a little more confusing to immediately 27 00:01:55,990 --> 00:02:03,070 be able to understand what is going on in this statement and something to relate this to programming. 28 00:02:03,070 --> 00:02:10,510 You could kind of replace the fruit in this sentence here with data, and it would be closely related 29 00:02:10,510 --> 00:02:13,150 to something that you might see in your code. 30 00:02:13,150 --> 00:02:19,150 So when you're having to write some programming problems, you might see something like this where instead 31 00:02:19,150 --> 00:02:26,890 of fruit, we're dealing with some type of input data or something like that, and we need to filter 32 00:02:26,890 --> 00:02:31,750 it out by using logic and turning that logic into code. 33 00:02:32,380 --> 00:02:39,190 So thankfully, there's ways that we can represent this and some rules that we can follow to make things 34 00:02:39,190 --> 00:02:40,210 a little simpler for us. 35 00:02:41,930 --> 00:02:44,600 So let's go ahead and try to analyze this statement. 36 00:02:44,630 --> 00:02:49,160 This is going to be slightly similar to when you decipher a word problems in math. 37 00:02:49,850 --> 00:02:55,490 So when you do that, you sometimes look for the important things in the word problem. 38 00:02:55,880 --> 00:03:00,650 And then you kind of go from there, you break it down and put it in simpler terms, more mathematical 39 00:03:00,650 --> 00:03:01,250 terms. 40 00:03:01,790 --> 00:03:02,720 We're going to do that. 41 00:03:02,720 --> 00:03:05,000 But it doesn't involve a ton of math, really. 42 00:03:05,450 --> 00:03:10,100 We're just going to kind of look at it and pick out words that have meaning for us as programmers. 43 00:03:11,690 --> 00:03:19,700 So they are colored here and have color coded the ones that are related, so we have an if so, that 44 00:03:19,700 --> 00:03:21,680 is a condition, right? 45 00:03:22,100 --> 00:03:30,230 So we're saying if Bob something also here, we're saying if both something. 46 00:03:31,490 --> 00:03:38,360 So we need to consider that, and then we have this doesn't and not. 47 00:03:38,510 --> 00:03:42,500 These are essentially the same things as kind of like not not right. 48 00:03:43,160 --> 00:03:47,420 If you were to simplify this and be like, well, doesn't is basically does not. 49 00:03:47,480 --> 00:03:49,340 So it's basically like another not. 50 00:03:49,880 --> 00:03:51,530 And we also have another not here. 51 00:03:52,790 --> 00:03:59,840 Also interesting is the and you know, so you got to think about when someone says this thing and that 52 00:03:59,840 --> 00:04:01,970 thing rather than just one thing. 53 00:04:02,990 --> 00:04:07,610 And then we also have an order here, you know, or implies this or implies either or. 54 00:04:07,880 --> 00:04:09,380 So red or yellow. 55 00:04:09,590 --> 00:04:12,740 So these are the important things that we need to look at their code here. 56 00:04:14,390 --> 00:04:16,210 So let's break it down a little bit further. 57 00:04:16,220 --> 00:04:18,990 Let's look at the words that we didn't color. 58 00:04:19,970 --> 00:04:30,770 So and kind of put them in some arbitrary terms, like some variables that we can actually use to simplify 59 00:04:30,770 --> 00:04:35,570 this and put it in a more kind of a mathematical definition. 60 00:04:35,570 --> 00:04:41,420 But, you know, don't freak out like it's going to be some kind of crazy equation or something. 61 00:04:41,420 --> 00:04:46,430 We're just going to try and represent all these words with variables so we can shorten this and not 62 00:04:46,430 --> 00:04:51,530 have to like think about all these different words, cause it didn't really matter whether it's watermelon 63 00:04:51,530 --> 00:04:53,540 or bananas or like, you know. 64 00:04:55,910 --> 00:05:01,810 You know, yeah, apples, whether they're available, it's just like, we can simplify this into a 65 00:05:01,820 --> 00:05:03,890 much more simple yes and no things. 66 00:05:05,020 --> 00:05:06,580 So that's what we're going to do. 67 00:05:06,850 --> 00:05:13,150 We're actually going to look at turning these into something that can be either be true or false and 68 00:05:13,150 --> 00:05:14,370 represent it with a variable. 69 00:05:14,380 --> 00:05:17,900 So this first one right here, Bob, have a watermelon. 70 00:05:18,700 --> 00:05:24,490 So I'm just going to turn and something that barely makes more sense, which is Bob has watermelon, 71 00:05:24,820 --> 00:05:29,020 should be a bob, has a watermelon, but I'm just putting Bob has watermelon, so that's something that 72 00:05:29,020 --> 00:05:30,280 can be true or false, right? 73 00:05:30,800 --> 00:05:34,670 Either Bob has a watermelon or Bob does not have a watermelon. 74 00:05:34,960 --> 00:05:38,620 We're just going to say there's this statement that can be said about it. 75 00:05:38,980 --> 00:05:43,780 Bob has a watermelon that is either true or it's false, and we're going to represent that with A.. 76 00:05:44,320 --> 00:05:45,490 Let's move on to the next one. 77 00:05:45,500 --> 00:05:45,880 So. 78 00:05:47,040 --> 00:05:49,680 He will get all bananas, so that's Bob, right? 79 00:05:50,310 --> 00:05:54,420 So Bob gets all bananas, we're going to represent that with B. 80 00:05:55,710 --> 00:05:57,660 And let's think about this whole sentence now. 81 00:05:57,660 --> 00:06:02,210 So this is kind of the thing that we're interested in, right? 82 00:06:02,220 --> 00:06:03,300 If you look at this sentence. 83 00:06:03,300 --> 00:06:04,320 So if Bob. 84 00:06:05,510 --> 00:06:06,320 Blah blah blah. 85 00:06:06,650 --> 00:06:14,660 And over here, if blah blah blah, then Bob gets all bananas basically, right? 86 00:06:15,200 --> 00:06:22,640 So these other parts of this sentence are kind of the conditions, and this is the result that's contingent 87 00:06:22,640 --> 00:06:24,290 upon those conditions, right? 88 00:06:25,730 --> 00:06:34,280 So Bob will not get all the bananas if this and if this part right here. 89 00:06:35,270 --> 00:06:40,040 So this is kind of the result, we're still going to represent it with a variable and we'll see how 90 00:06:40,040 --> 00:06:41,030 it plays into it. 91 00:06:42,320 --> 00:06:44,630 So that's going to be be Bob getting all bananas. 92 00:06:46,200 --> 00:06:48,090 Then we have this next part, so. 93 00:06:49,450 --> 00:06:58,230 Orange is right, if it says if both oranges and love are available, right, so the oranges are available, 94 00:06:58,240 --> 00:07:00,850 that's another statement that we can take out of this. 95 00:07:01,660 --> 00:07:08,740 All of these things right here, these fruits are kind of having to do with the fact that they are available, 96 00:07:09,010 --> 00:07:09,340 right? 97 00:07:10,570 --> 00:07:14,770 So we're going to put a see for oranges are available. 98 00:07:17,350 --> 00:07:19,230 Same thing with the apples, right? 99 00:07:19,240 --> 00:07:27,400 And this is specifically we have red or yellow apples, so I'm going to say D is red apples are available 100 00:07:28,150 --> 00:07:29,260 just like the oranges. 101 00:07:29,710 --> 00:07:32,830 And then also for the yellow yellow apples are available. 102 00:07:32,830 --> 00:07:37,720 So you see, we're just continuing to write these statements here that can be seen as true or false. 103 00:07:39,270 --> 00:07:41,250 A kind of contingent on things, you know? 104 00:07:42,970 --> 00:07:51,970 OK, so now let's break it down a little more and kind of turn it into an expression that is a little 105 00:07:51,970 --> 00:07:57,820 bit more kind of mathematical or really what it's like is a. 106 00:07:58,930 --> 00:08:01,240 Kind of simplified version of code. 107 00:08:01,690 --> 00:08:10,450 So this is something that you can call pseudocode not quite exact C++ code, but something that we can 108 00:08:10,450 --> 00:08:13,530 think of in terms of code. 109 00:08:13,540 --> 00:08:23,560 So we're trying to break a normal spoken sentence, written sentence into more of an exact kind of scientific 110 00:08:23,560 --> 00:08:24,750 definition, if you will. 111 00:08:25,880 --> 00:08:27,260 So what do we start out with? 112 00:08:28,610 --> 00:08:35,030 It's basically if Bob does not have a watermelon, right, we can simplify that with the variables and 113 00:08:35,030 --> 00:08:39,410 kind of, you know, we simplify this doesn't not as well. 114 00:08:39,410 --> 00:08:41,660 So we have this if here, right? 115 00:08:41,660 --> 00:08:47,050 We say, if not, not a so doesn't not is not not. 116 00:08:47,060 --> 00:08:51,260 And then we have this issue here in the beginning and a is Bob has a watermelon, right? 117 00:08:52,710 --> 00:08:57,600 So this is if Bob does not have watermelon is going to be, if not, not a. 118 00:08:58,650 --> 00:08:59,940 So let's look at the next part. 119 00:09:01,490 --> 00:09:06,710 So we basically have C, which is oranges are available, that's the next part, and, you know, I've 120 00:09:06,710 --> 00:09:09,920 kind of ignore I kind of left this purple. 121 00:09:11,140 --> 00:09:16,420 Thing highlighted, so don't associate what we're talking about right now, like each piece of this 122 00:09:16,420 --> 00:09:19,210 to be with the purple I kind of just by accident left that there. 123 00:09:20,140 --> 00:09:25,600 So if C C is oranges are available, right, so we have this f right here. 124 00:09:28,210 --> 00:09:33,910 So basically, we have the first air freight, so if Bob does not have a watermelon. 125 00:09:35,070 --> 00:09:42,030 And then we said he will not get all bananas if, but we also we basically have this condition right 126 00:09:42,030 --> 00:09:42,540 here. 127 00:09:44,240 --> 00:09:48,590 Or they already had it kind of be fulfilled if I didn't have a watermelon, he's definitely not going 128 00:09:48,590 --> 00:09:49,630 to get it. 129 00:09:49,640 --> 00:09:52,520 Bob doesn't not have a watermelon, he definitely is not going to. 130 00:09:54,910 --> 00:09:57,800 He is definitely not not going to get all the bananas. 131 00:09:57,820 --> 00:09:59,590 You know, he's going to get the bananas. 132 00:09:59,950 --> 00:10:07,750 So if this is fulfilled, then we can kind of look to see if this next thing is all fulfilled. 133 00:10:08,350 --> 00:10:13,120 The second, if everything that comes after the second half is fulfilled and if those odds are fulfilled, 134 00:10:13,420 --> 00:10:15,240 then this will be true. 135 00:10:15,250 --> 00:10:17,320 This whole thing right here will be true. 136 00:10:19,090 --> 00:10:19,570 So. 137 00:10:20,940 --> 00:10:21,930 That's kind of what we're doing. 138 00:10:21,990 --> 00:10:27,060 Breaking it down, so we basically look at this first thing right here, so we need to check first whether 139 00:10:27,060 --> 00:10:29,520 Bob doesn't not have a watermelon, right? 140 00:10:30,240 --> 00:10:36,510 If that gets fulfilled, if this turns out to be true, then we can look at this second condition right 141 00:10:36,510 --> 00:10:36,990 here. 142 00:10:37,110 --> 00:10:39,720 It starts with this if it is the rest of this sentence. 143 00:10:40,930 --> 00:10:47,140 And if that turns out to be true, then we can say that this whole thing I'm circling right here would 144 00:10:47,140 --> 00:10:48,100 be true, right? 145 00:10:49,270 --> 00:10:54,640 That's kind of the contingencies for Bob to not get all bananas, right? 146 00:10:55,630 --> 00:10:56,080 So. 147 00:10:57,340 --> 00:11:04,330 We're now going to continue with this, we have the AFC for it, that's if we had to if both oranges, 148 00:11:04,330 --> 00:11:08,260 but remember, we represent see with oranges are available. 149 00:11:08,260 --> 00:11:16,390 So we're saying if the oranges are available and because we have this ad right here and then we're saying 150 00:11:16,390 --> 00:11:17,080 de. 151 00:11:18,100 --> 00:11:19,680 Or E! 152 00:11:20,110 --> 00:11:22,420 Which is red apples are available. 153 00:11:22,820 --> 00:11:26,560 Or yellow apples are available, right? 154 00:11:28,290 --> 00:11:34,560 So that's why we're in this whole second thing, starting at this, if this whole second section of 155 00:11:34,560 --> 00:11:36,450 the sentence is if. 156 00:11:37,430 --> 00:11:40,250 Oranges are available and. 157 00:11:42,040 --> 00:11:49,900 Red apples are available or yellow apples are available, and this is kind of like a little subsection 158 00:11:49,900 --> 00:11:50,900 of the sentence, right? 159 00:11:50,920 --> 00:11:57,850 So we're saying if both oranges and and then we got to look at this whole thing, red or yellow apples 160 00:11:57,850 --> 00:11:58,420 are available. 161 00:11:58,420 --> 00:12:02,050 So that is saying red apples are available or yellow apples are available. 162 00:12:03,030 --> 00:12:05,400 So we simplify that and the D or E. 163 00:12:05,430 --> 00:12:08,690 So we have F C and D Ori. 164 00:12:10,070 --> 00:12:14,570 So if all of this gets fulfilled, this thing turns out to be true. 165 00:12:15,020 --> 00:12:27,050 And then this all turns out to be true, then we can say B, which is Bob gets all bananas will be false, 166 00:12:27,050 --> 00:12:27,260 right? 167 00:12:27,260 --> 00:12:32,360 Because we said he will not get all bananas if this and if this. 168 00:12:33,890 --> 00:12:40,670 So this turned out to be true, this turns out to be true, then we say this thing I'm circling is true. 169 00:12:42,080 --> 00:12:48,830 But we're saying that B is false because we called B Bob gets all bananas, but this thing that I'm 170 00:12:48,830 --> 00:12:50,720 circling is true, which has a knot in it. 171 00:12:50,870 --> 00:12:52,580 He says he will not get all the bananas. 172 00:12:52,610 --> 00:12:55,460 It is true that Bob will not get all the bananas. 173 00:12:55,460 --> 00:13:01,910 So that's why since B was Bob gets all bananas were saying B is going to be false because it's the opposite, 174 00:13:01,910 --> 00:13:02,090 right? 175 00:13:02,090 --> 00:13:05,120 We said it's true that Bob will not get all the bananas. 176 00:13:06,630 --> 00:13:10,260 So maybe a little confusing, but try and break it down for you here. 177 00:13:10,710 --> 00:13:18,210 This is kind of what we do when we encounter a word problem, a logic kind of problem and we need to 178 00:13:18,240 --> 00:13:19,590 turn it into code. 179 00:13:19,620 --> 00:13:25,770 We got to go through this process of turning it into code, and this is kind of the initial stage is 180 00:13:25,770 --> 00:13:27,450 turning it into something like this. 181 00:13:28,410 --> 00:13:35,010 After that, then you would move on to transitioning from this into actual C++ code or whatever coding 182 00:13:35,010 --> 00:13:35,820 language you're using. 183 00:13:36,330 --> 00:13:39,170 We're going to break this down further, though, because we're not quite done yet. 184 00:13:39,180 --> 00:13:45,750 I kind of just told you how to arrange this, but we need to talk about these individual components, 185 00:13:45,750 --> 00:13:47,640 like if we were to say. 186 00:13:48,630 --> 00:13:51,840 That a was true. 187 00:13:52,200 --> 00:13:53,550 Or C. 188 00:13:54,500 --> 00:14:00,710 Was false, and D was true, but E was false or something like that, you know, like rub out right? 189 00:14:00,710 --> 00:14:06,530 Apples aren't available, but yellow apples are available, but oranges aren't available and Bob does 190 00:14:06,530 --> 00:14:08,150 have a watermelon, you know, things like that. 191 00:14:08,630 --> 00:14:15,680 We need to, like, put some information into these true false kind of questions and then figure out 192 00:14:15,680 --> 00:14:17,770 what all the different answers could be. 193 00:14:17,780 --> 00:14:19,970 If we said yes, a is true. 194 00:14:20,440 --> 00:14:21,680 ABC is not true. 195 00:14:22,040 --> 00:14:23,560 D is true. 196 00:14:23,570 --> 00:14:25,700 E is not true, you know, stuff like that. 197 00:14:27,050 --> 00:14:28,190 So let's take a look at that. 198 00:14:28,700 --> 00:14:33,110 This is actually having a lot to do with Boolean values, which I know is already mentioned to you in 199 00:14:33,110 --> 00:14:35,000 the data types section. 200 00:14:35,000 --> 00:14:41,960 So if you remember the short slide on that, it did talk about how Boolean values are true and false 201 00:14:41,960 --> 00:14:42,710 values, right? 202 00:14:42,980 --> 00:14:48,890 There can be variables in your code that are true or false values, which are the same things as one 203 00:14:48,890 --> 00:14:50,840 in zero, right? 204 00:14:50,840 --> 00:14:51,260 So. 205 00:14:52,310 --> 00:14:57,980 When we rearrange these normal statements that we had like that sentence into a collection of true and 206 00:14:57,980 --> 00:15:05,600 false statements, then we're able to move to creating some code that can filter an output based on 207 00:15:05,600 --> 00:15:09,050 those if conditions when the data comes in and we say, Hey. 208 00:15:10,220 --> 00:15:14,510 A is true or B is true or, you know, C is false stuff like that. 209 00:15:15,680 --> 00:15:21,980 When we build these things like this right here, then we're able to kind of filter out a total result, 210 00:15:21,980 --> 00:15:22,340 right? 211 00:15:22,370 --> 00:15:25,580 With these different combinations of Boolean values, they come in. 212 00:15:25,580 --> 00:15:26,990 So we made variables right. 213 00:15:27,000 --> 00:15:28,940 We have a is a variable b c. 214 00:15:29,630 --> 00:15:32,270 Each one of those is a Boolean variable. 215 00:15:32,450 --> 00:15:36,170 It's a Boolean value stored inside that variable, and it's either true or false. 216 00:15:37,230 --> 00:15:42,210 And then a big, important thing to connect to it is the fact that in computer science, when we're 217 00:15:42,210 --> 00:15:49,560 talking about true, that is synonymous with one, we talk about false that is synonymous with zero. 218 00:15:49,950 --> 00:15:51,780 Same kind of thing in binary. 219 00:15:51,780 --> 00:15:54,390 Right on, off on off. 220 00:15:54,420 --> 00:15:55,100 True. 221 00:15:55,230 --> 00:15:55,900 False. 222 00:15:55,920 --> 00:15:57,210 One zero. 223 00:15:58,020 --> 00:15:59,250 Connect all those things. 224 00:15:59,250 --> 00:16:00,120 They're all the same. 225 00:16:00,120 --> 00:16:01,050 They mean the same thing.