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.