Consider the following Boolean expressions. A && B
!A && !B
Which of the following best describes the relationship between values produced by expression I and expression II?
(A) Expression I and expression II evaluate to different values for all values of A and B.
(B) Expression and expression II evaluate to the same value for all values of A and B.
(C) Expression and expression II evaluate to the same value only when A and B are the same.
(D) Expression and expression Il evaluate to the same value only when A and B differ.
(E) Expression I and expression Il evaluate to the same value whenever A is true.

(D) Expression I and expression Il evaluate to the same value only when A and B differ.

Explanation:

Given

Required

Select the true statement

To do this, I will create the following case scenarios.

(a): and

i.e. true and true is true

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So, we have:

So:

 and

Hence, options (B) and (E) are incorrect

(b): and

Solve each negation

So:

 and

Hence, option (c) is incorrect

(c): and

So:

  and

Case scenarios b and c implies that option (d) is correct because different values of A and B gives the same value of both expression which is false

This also implies that (a) is incorrect.