The binary operation □ is defined as follows:

P | Q | P □ Q
T | T | T
T | F | F
F | T | T
F | F | T

Which one of the f...

Question

The binary operation □ is defined as follows:

P | Q | P □ Q
T | T | T
T | F | F
F | T | T
F | F | T

Which one of the following is equivalent to P □ Q?

A. ~(C -> P)
B. ~(P ^ ~Q)
C. P ^ Q
D. ~P ^ Q

Accepted Answer

P □ Q is equivalent to P -> Q = ~(P ^ ~Q), so the answer is B. Read the truth table row by row: the operation P □ Q gives T whenever Q is T or P is F, and only gives F when P is T and Q is F. This is exactly the same as the implication P -> Q. The formula ~(P ^ ~Q) is the negation of 'P is true and Q is false', which is another standard way to write P -> Q. So option B is equivalent.

The binary operation □ is defined as follows: P | Q | P □ Q T | T | T T | F | F F | T | T F | F | T Which one of the following is equivalent to P □ Q? A. ~(C -> P) B. ~(P ^ ~Q) C. P ^ Q D. ~P ^ Q