Considering the boolean expression, is (A AND B)' OR C equal to (A' AND B') OR C

Answer 1

Answer: These boolean expressions are not the same. By creating a truth table for both, we can see that the truth tables do not match.

A truth table is when we take every possible combination of true and false for all values in a given boolean expression.

In order for these boolean expressions to be considered the same, their truth tables must match. See the attached tables.

Truth table for !(A and B) or C:

A B C Result

F F F T

F F T T

F T F T

F T T T

T F F T

T F T T

T T F F

T T T T

Truth table for (!A and !B) or C:

A B C Result

F F F T

F F T T

F T F F

F T T T

T F F F

T F T T

T T F F

T T T T

As you can see, the truth tables don't match. So we can say that the expressions do not match. If you were doing this on a test, you can stop making the truth table as soon as you get to two sets of values that do not match. For example, you could stop after testing only 3 values in each expression because on the third set of values, the first expression returns true while the other returns false.

Hopefully this helps :)