Exercise
The following table shows the value of an expression based on the values of a and b.
Value of a |
Value of b |
Value of expression |
|---|---|---|
true |
true |
true |
true |
false |
false |
false |
true |
true |
false |
false |
true |
Which of the following expressions are equivalent to the value of the expression shown in the table?
Select TWO answers.
(A) NOT (a AND b)
(B) NOT (a OR b)
(C) NOT (a AND (NOT b))
(D) (NOT a) OR b
Solution
(C) NOT (a AND (NOT b))
(D) (NOT a) OR b
The expression evaluates to false if and only if a is true and b is false.
Write the expression as if it evaluated to true under the circumstances above.
a AND (NOT b)
Add a NOT outside to make the expression false.
NOT (a AND (NOT b))
This is one of the answer choices.
Distributing the NOT yields:
(NOT a) OR NOT(NOT b)
(NOT a) OR b
This is the other correct answer choice.