c++ - Simplify these boolean expressions? -


i not sure if simplifying these boolean expressions correctly:

1. (a && b) || b 2. (a || b) && 3. !(a || b) && 4. !(a && b) || !b

simplified expressions:

1. && b 2. || b 3. !b && 4. !a || !b

fairly easy sort out truth tables

1. (a && b) || b  b | e 0 0 | 0 0 1 | 1 1 0 | 0 1 1 | 1  simplified: b ################ 2. (a || b) &&  b | e 0 0 | 0 0 1 | 0 1 0 | 1 1 1 | 1  simplified:  algebraically: using our identity we've derived part 1: (a || b) && --> (a && a) || (a && b) --> || (a && b) --> ################# 3. !(a || b) &&  b | e 0 0 | 0 0 1 | 0 1 0 | 0 1 1 | 0  simplified: 0  algebraically (via demorgans) !(a||b)&&a --> (!a && !b)  && --> !a && !b && --> (a && !a) && !b --> 0 && !b --> 0  ################## 4. !(a && b) || !b b | e 0 0 | 1 0 1 | 1 1 0 | 1 1 1 | 0  simplified: !a || !b

most of these can done algebraically well, truth tables make life easy.


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