WEBVTT 00:00.550 --> 00:07.790 Want to go over a very important concept in programming called boolean logic using Poulan logic to create 00:07.820 --> 00:15.530 our conditions which in turn will make our decisions we said before that conditions can either evaluate 00:15.530 --> 00:17.380 to TRUE or FALSE. 00:17.390 --> 00:26.840 So your own two values a boolean Bayrou variable can have is what and logic really boils down to getting 00:26.840 --> 00:32.200 things to evaluate to TRUE or FALSE. 00:32.450 --> 00:39.630 There are three main operations we'll go through and or and inverse. 00:39.760 --> 00:50.370 So for and logical and here say we have to in variables A and B. 00:50.810 --> 00:59.100 So the whole condition evaluates to true only if A and B are both true. 00:59.970 --> 01:04.860 So otherwise the combination is false. 01:05.540 --> 01:11.570 So this makes sense if you really think about it both have to be true in order for the entire thing 01:11.570 --> 01:12.390 to be true. 01:15.370 --> 01:25.510 So the next is Wanjiku or so again we say we have our boolean values a and b. 01:25.750 --> 01:31.750 So a or b is true if either is true. 01:31.750 --> 01:39.400 So either A is true or B is true or both a and b are true. 01:39.400 --> 01:48.280 So the only time a or b is false is if A is false and B is false. 01:48.280 --> 01:52.050 So the exact opposite of and 01:55.070 --> 01:56.450 so inverse. 01:56.460 --> 02:02.620 Let's say we have a is a in value and you sign it to be true. 02:02.990 --> 02:07.900 So the inverse of A then is false and vice versa. 02:07.910 --> 02:18.300 Say we add a is false the inverse a would be true it's just the opposite of what the value is. 02:18.300 --> 02:22.940 So there are a few laws that you can use and think about. 02:23.160 --> 02:31.010 And the first one is the associate of law also a or b is the same as B or A. 02:31.080 --> 02:39.330 And of course the same for and is a and b is the same as B and C you can write them in any order. 02:39.340 --> 02:41.850 It's really what this is saying. 02:44.880 --> 02:55.780 The distributive law so let's say we have a and in parentheses B or C is the same as saying a and b 02:55.930 --> 03:04.200 or a and c so it distributes to each part of the expression 03:08.470 --> 03:11.640 so and laso see me have a. 03:12.030 --> 03:13.590 And false. 03:13.590 --> 03:21.540 Well we said before both have to be true for the entire expression to be true so a and false is always 03:21.540 --> 03:22.480 false. 03:23.350 --> 03:26.110 So a and true. 03:26.170 --> 03:33.100 Well that really depends on what a is if a is true then the whole expression of it be true. 03:33.100 --> 03:47.840 But if a was false false and true is false A and A is again really just dependent on what A is and similarly 03:48.260 --> 03:54.800 A and B inverse of A is always false because a can't have the value. 03:54.890 --> 04:01.030 So if A has a value true and inverse of true is false. 04:01.040 --> 04:04.720 So a true and false is false. 04:04.720 --> 04:10.720 So it can't be both true. 04:10.910 --> 04:17.140 So the or law say we have a. 04:17.170 --> 04:18.110 Or false. 04:18.110 --> 04:21.580 Well again it depends on what A is. 04:21.610 --> 04:29.050 So if A was true then the entire expression true if A was false then the entire expression would be 04:29.050 --> 04:31.220 false. 04:31.300 --> 04:34.180 And similarly with the A or true. 04:34.180 --> 04:43.600 Well you said before that if either part of the expression is true then offering it together is always 04:43.600 --> 04:44.150 true. 04:46.070 --> 04:52.600 And then a or a is again always a depends and then a. 04:52.650 --> 04:56.910 Or should say the inverse of A is always true. 04:56.910 --> 05:08.100 So it's the opposite of what the analysts said because say was false A or the inverse of false is true. 05:08.130 --> 05:09.110 So for 05:12.020 --> 05:15.130 and lastly the in version on. 05:15.440 --> 05:21.490 Let's say we have the inverse of the inverse of a well the inverse is just kind of cancel out. 05:21.530 --> 05:26.960 And then you're left with Hey. 05:27.220 --> 05:33.120 There there are some other ways something can evaluate to TRUE and FALSE and we'll see that in the next 05:33.120 --> 05:33.920 lecture. 05:34.170 --> 05:40.740 We also see some examples of what I just outlined in the next lecture and what the syntax we need to 05:40.740 --> 05:43.180 make this to make this work.