WEBVTT 1 00:00:01.310 --> 00:00:03.780 When we learn about if-else statements, 2 00:00:03.780 --> 00:00:06.290 comparison and equality operators 3 00:00:06.290 --> 00:00:07.910 and Boolean values. 4 00:00:07.910 --> 00:00:10.630 We also need to learn about logic. 5 00:00:10.630 --> 00:00:13.710 And in particular about Boolean logic. 6 00:00:13.710 --> 00:00:16.133 So let's do that in this video. 7 00:00:17.580 --> 00:00:20.090 So basically Boolean logic 8 00:00:20.090 --> 00:00:22.220 is a branch of computer science, 9 00:00:22.220 --> 00:00:24.430 which uses true and false values 10 00:00:24.430 --> 00:00:27.340 to solve complex logical problems. 11 00:00:27.340 --> 00:00:28.820 And in order to do that, 12 00:00:28.820 --> 00:00:31.200 it uses several logical operators 13 00:00:31.200 --> 00:00:34.130 to combine true and false values. 14 00:00:34.130 --> 00:00:36.680 So much like we use arithmetic operators, 15 00:00:36.680 --> 00:00:38.990 to combine numeric values. 16 00:00:38.990 --> 00:00:41.530 Now we're only going to scratch the surface here 17 00:00:41.530 --> 00:00:44.840 and talk about the most basic logical operators, 18 00:00:44.840 --> 00:00:48.480 which are the AND, OR, and NOT operators. 19 00:00:48.480 --> 00:00:50.490 And note that Boolean logic 20 00:00:50.490 --> 00:00:53.670 is actually not specific to JavaScript. 21 00:00:53.670 --> 00:00:56.670 This is all true for all programming. 22 00:00:56.670 --> 00:00:57.503 But anyway, 23 00:00:57.503 --> 00:01:00.260 let's now understand how these operators work 24 00:01:00.260 --> 00:01:03.710 and use an example to illustrate it. 25 00:01:03.710 --> 00:01:06.460 So here we have two Boolean variables 26 00:01:06.460 --> 00:01:09.440 that can either be true or false. 27 00:01:09.440 --> 00:01:13.120 So A is that Sarah has a driver's license 28 00:01:13.120 --> 00:01:15.900 and B is that Sarah has good vision. 29 00:01:15.900 --> 00:01:18.520 So both of these are of course conditions, 30 00:01:18.520 --> 00:01:20.580 that can be true or false 31 00:01:20.580 --> 00:01:23.210 because Sarah could have no driver's license 32 00:01:23.210 --> 00:01:25.380 and she could have no good vision, 33 00:01:25.380 --> 00:01:26.340 right. 34 00:01:26.340 --> 00:01:28.070 And of course on the other hand, 35 00:01:28.070 --> 00:01:30.190 she could also have a driver's license 36 00:01:30.190 --> 00:01:32.620 and could have good vision. 37 00:01:32.620 --> 00:01:36.800 Now using the AND operator like A aND B, 38 00:01:36.800 --> 00:01:38.940 we can combine these two Boolean variables 39 00:01:38.940 --> 00:01:43.510 like Sarah has a driver's license and good vision. 40 00:01:43.510 --> 00:01:44.343 Okay. 41 00:01:44.343 --> 00:01:47.860 But now what will be the result of this operation? 42 00:01:47.860 --> 00:01:48.950 Well for that, 43 00:01:48.950 --> 00:01:51.370 we use a so-called truth table, 44 00:01:51.370 --> 00:01:53.880 which looks something like this. 45 00:01:53.880 --> 00:01:55.860 Here we have to two possible values 46 00:01:55.860 --> 00:01:57.230 for each of the variables, 47 00:01:57.230 --> 00:01:58.380 A AND B, 48 00:01:58.380 --> 00:02:02.580 which gives us four possible combinations of results. 49 00:02:02.580 --> 00:02:04.190 And so then all we have to do 50 00:02:04.190 --> 00:02:06.909 is to plug in the value of our variables, 51 00:02:06.909 --> 00:02:09.790 and to get a result of the AND operation 52 00:02:09.790 --> 00:02:11.290 from this table. 53 00:02:11.290 --> 00:02:13.740 So what we can see from this table 54 00:02:13.740 --> 00:02:17.150 is that only if both A and B are true, 55 00:02:17.150 --> 00:02:20.940 the result of the operation will be true as well. 56 00:02:20.940 --> 00:02:23.060 And that makes sense, right! 57 00:02:23.060 --> 00:02:23.950 After all, 58 00:02:23.950 --> 00:02:26.260 it's called the AND operator. 59 00:02:26.260 --> 00:02:27.310 And so again, 60 00:02:27.310 --> 00:02:29.190 what the AND operator does 61 00:02:29.190 --> 00:02:30.850 is to return true 62 00:02:30.850 --> 00:02:34.320 only if both A AND B are true. 63 00:02:34.320 --> 00:02:35.910 In all other situations, 64 00:02:35.910 --> 00:02:38.730 if either A or B are false, 65 00:02:38.730 --> 00:02:41.750 then A AND B will also be false. 66 00:02:41.750 --> 00:02:44.680 And we can also generalize this to more operands. 67 00:02:44.680 --> 00:02:47.150 So to more than just two values, 68 00:02:47.150 --> 00:02:49.870 we could do A AND B AND C, 69 00:02:49.870 --> 00:02:51.430 and results would be true 70 00:02:51.430 --> 00:02:54.320 only if all of them are true. 71 00:02:54.320 --> 00:02:55.920 And if one of them is false, 72 00:02:55.920 --> 00:02:59.870 then the result is immediately false as well. 73 00:02:59.870 --> 00:03:01.680 Now I know that all of this, 74 00:03:01.680 --> 00:03:04.360 might look a little bit confusing, 75 00:03:04.360 --> 00:03:06.700 but don't worry We will have an example, 76 00:03:06.700 --> 00:03:08.710 a little bit later in this lecture, 77 00:03:08.710 --> 00:03:10.830 and we will also use this in practice 78 00:03:10.830 --> 00:03:12.140 and the next one. 79 00:03:12.140 --> 00:03:13.210 And after some practice, 80 00:03:13.210 --> 00:03:15.340 you will internalize all of this 81 00:03:15.340 --> 00:03:18.239 and you won't even need any truth tables. 82 00:03:18.239 --> 00:03:19.710 Now moving on, 83 00:03:19.710 --> 00:03:20.599 on the other hand, 84 00:03:20.599 --> 00:03:23.670 we also have the OR operator, 85 00:03:23.670 --> 00:03:26.380 which kind of works in the opposite way. 86 00:03:26.380 --> 00:03:28.210 So with our current example, 87 00:03:28.210 --> 00:03:29.970 we could use the OR operator 88 00:03:29.970 --> 00:03:31.820 to determine whether Sarah 89 00:03:31.820 --> 00:03:35.000 has a driver's license or good vision. 90 00:03:35.000 --> 00:03:37.120 And just by thinking about this, 91 00:03:37.120 --> 00:03:39.620 we can already intuitively imagine 92 00:03:39.620 --> 00:03:41.960 that the OR operator will be true 93 00:03:41.960 --> 00:03:44.710 if just one of the variables is true. 94 00:03:44.710 --> 00:03:45.640 And in fact, 95 00:03:45.640 --> 00:03:50.170 a look at the truth table confirms exactly that. 96 00:03:50.170 --> 00:03:53.850 So unlike the AND operator and the OR operator, 97 00:03:53.850 --> 00:03:56.400 even if one of the variables is false, 98 00:03:56.400 --> 00:03:59.130 the outcome will still be true. 99 00:03:59.130 --> 00:04:00.380 Or in other words, 100 00:04:00.380 --> 00:04:02.830 if either A OR B is true, 101 00:04:02.830 --> 00:04:05.780 then the OR operation becomes true as well. 102 00:04:05.780 --> 00:04:08.900 And that's why it's called the OR operator. 103 00:04:08.900 --> 00:04:10.230 And once more, 104 00:04:10.230 --> 00:04:12.260 if we have multiple variables, 105 00:04:12.260 --> 00:04:15.010 it's enough for one of them to be true, 106 00:04:15.010 --> 00:04:18.360 to make the whole operation become true as well. 107 00:04:18.360 --> 00:04:20.660 Okay, I hope this makes sense. 108 00:04:20.660 --> 00:04:21.810 And once again, 109 00:04:21.810 --> 00:04:22.980 I can assure you 110 00:04:22.980 --> 00:04:24.480 that it will make sense 111 00:04:24.480 --> 00:04:27.840 once we start using this in practice. 112 00:04:27.840 --> 00:04:28.673 Anyway, 113 00:04:28.673 --> 00:04:31.830 we finally also have the NOT operator, 114 00:04:31.830 --> 00:04:33.360 which is a lot simpler 115 00:04:33.360 --> 00:04:36.060 because it doesn't combine multiple values. 116 00:04:36.060 --> 00:04:36.990 Instead, 117 00:04:36.990 --> 00:04:40.920 the NOT operator acts on only one Boolean value 118 00:04:40.920 --> 00:04:43.420 and it basically just inverts it. 119 00:04:43.420 --> 00:04:44.910 So if A is true, 120 00:04:44.910 --> 00:04:46.270 it will become false. 121 00:04:46.270 --> 00:04:47.400 And if it's false, 122 00:04:47.400 --> 00:04:49.720 then NOT A will become true, 123 00:04:49.720 --> 00:04:51.400 simple as that. 124 00:04:51.400 --> 00:04:52.320 And that's basically 125 00:04:52.320 --> 00:04:56.200 how these three most important logical operators work. 126 00:04:56.200 --> 00:04:57.033 But of course, 127 00:04:57.033 --> 00:04:58.670 the best way to understand it 128 00:04:58.670 --> 00:05:01.640 is to use a more practical example. 129 00:05:01.640 --> 00:05:03.280 So let's go again back 130 00:05:03.280 --> 00:05:04.372 to using the age, 131 00:05:04.372 --> 00:05:07.600 and this time we set it to 16. 132 00:05:07.600 --> 00:05:08.737 And then we have, 133 00:05:08.737 --> 00:05:10.800 our two Boolean variables. 134 00:05:10.800 --> 00:05:14.630 The first one is age is greater or equal 20. 135 00:05:14.630 --> 00:05:18.660 And the second one is age is less than 30. 136 00:05:18.660 --> 00:05:21.580 So let's determine the value of each of them. 137 00:05:21.580 --> 00:05:23.072 So if age is 16, 138 00:05:23.072 --> 00:05:26.021 then age is greater or equal to any 139 00:05:26.021 --> 00:05:27.611 must be false. 140 00:05:27.611 --> 00:05:28.462 Right! 141 00:05:28.462 --> 00:05:29.950 And of course it is, 142 00:05:29.950 --> 00:05:32.533 and age is less than 30 is true 143 00:05:33.735 --> 00:05:37.642 because 16 obviously is less than 30. 144 00:05:37.642 --> 00:05:38.664 Okay. 145 00:05:38.664 --> 00:05:40.390 So that's the baseline basically, 146 00:05:40.390 --> 00:05:42.330 and now we will start to combine 147 00:05:42.330 --> 00:05:44.110 these variables A and B 148 00:05:44.110 --> 00:05:46.760 using some logical operators. 149 00:05:46.760 --> 00:05:48.630 So the first exercise 150 00:05:48.630 --> 00:05:50.350 is the NOT operator. 151 00:05:50.350 --> 00:05:51.510 So NOT A, 152 00:05:51.510 --> 00:05:56.070 and we know right now that A is false, right? 153 00:05:56.070 --> 00:05:57.970 So the result of NOT A, 154 00:05:57.970 --> 00:06:00.610 as we just learned is true, 155 00:06:00.610 --> 00:06:01.650 because all it does 156 00:06:01.650 --> 00:06:05.570 is to invert the logical value of the variable. 157 00:06:05.570 --> 00:06:08.190 Next one we have A AND B, 158 00:06:08.190 --> 00:06:12.060 now we already know that A is false and B is true. 159 00:06:12.060 --> 00:06:14.010 So I'm just putting these values here again, 160 00:06:14.010 --> 00:06:16.100 to make it a bit easier to follow. 161 00:06:16.100 --> 00:06:17.010 Okay. 162 00:06:17.010 --> 00:06:20.200 So we have basically false and true. 163 00:06:20.200 --> 00:06:22.650 So from a look at our truth table here 164 00:06:22.650 --> 00:06:23.830 at the right side, 165 00:06:23.830 --> 00:06:25.130 we can easily determine 166 00:06:25.130 --> 00:06:28.600 that the result of this must be false. 167 00:06:28.600 --> 00:06:29.550 And so that's exactly 168 00:06:29.550 --> 00:06:31.020 what we learned before. 169 00:06:31.020 --> 00:06:32.890 So when we have the AND operator, 170 00:06:32.890 --> 00:06:36.000 it's enough for one of the operands to be false, 171 00:06:36.000 --> 00:06:39.392 to make the result of the operation also false. 172 00:06:39.392 --> 00:06:42.050 Now we have A OR B, 173 00:06:42.050 --> 00:06:46.010 and so let's check out the truth table in this case. 174 00:06:46.010 --> 00:06:47.740 And so in this case, 175 00:06:47.740 --> 00:06:49.920 we actually get true. 176 00:06:49.920 --> 00:06:52.380 And so this shows that it is enough 177 00:06:52.380 --> 00:06:54.600 for one variable to be true 178 00:06:54.600 --> 00:06:57.023 for the whole expression to be true as well. 179 00:06:58.620 --> 00:07:02.210 Next up let's check NOT A AND B. 180 00:07:02.210 --> 00:07:03.430 And we already know 181 00:07:03.430 --> 00:07:07.300 that NOT A is true and B is true. 182 00:07:07.300 --> 00:07:09.170 And so at this time for the first time, 183 00:07:09.170 --> 00:07:12.260 we are combining multiple operators here 184 00:07:12.260 --> 00:07:16.030 and yeah we already know that true and true 185 00:07:16.030 --> 00:07:18.900 will of course be true as well. 186 00:07:18.900 --> 00:07:22.560 And now another one combining two operators, 187 00:07:22.560 --> 00:07:25.640 so A OR NOT B. 188 00:07:25.640 --> 00:07:27.200 And just as a side note, 189 00:07:27.200 --> 00:07:30.570 the NOT operator actually has proceedings 190 00:07:30.570 --> 00:07:33.400 over the OR and AND operators. 191 00:07:33.400 --> 00:07:36.510 So basically the values are inverted first 192 00:07:36.510 --> 00:07:40.920 and only then they are combined using AND or OR. 193 00:07:40.920 --> 00:07:45.920 So we know that A is false and B is true. 194 00:07:46.190 --> 00:07:49.360 So NOT B must be false, right 195 00:07:49.360 --> 00:07:53.880 then false OR false is also false. 196 00:07:53.880 --> 00:07:56.170 And actually that's the only way in which 197 00:07:56.170 --> 00:07:58.270 the OR operator can be false. 198 00:07:58.270 --> 00:08:00.343 If all of them are false basically. 199 00:08:01.450 --> 00:08:03.990 So I hope that made sense to you. 200 00:08:03.990 --> 00:08:05.720 And so in the next lecture, 201 00:08:05.720 --> 00:08:09.700 we will actually use these operators in a code. 202 00:08:09.700 --> 00:08:13.290 And then it will make even more sense to you. 203 00:08:13.290 --> 00:08:14.420 So by then, 204 00:08:14.420 --> 00:08:18.310 we probably won't even need the truth tables anymore, 205 00:08:18.310 --> 00:08:20.550 because it will become quite intuitive 206 00:08:20.550 --> 00:08:23.930 how both of these operators actually work. 207 00:08:23.930 --> 00:08:25.870 But anyway, let's now move on 208 00:08:25.870 --> 00:08:27.873 and I see you in the next video.