Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-{X $ \lor $ [C • (Y ⊃ B)]} ⊃ {Z ⊃ [Z ⊃ (Z ⊃ Z)]}
A) True
B) False
C) Unknown

Question

Quizplus · Accepted Answer

Starting from the left side of the expression:
{X $ \lor $ [C • (Y ⊃ B)]}
Since X is false, the first part of the expression is false. 
For the second part, since all premises are true, we only need to evaluate (Y ⊃ B) which is false because Y is false (and anything follows from false), therefore the entire expression in the brackets is false. 
So, we have false $ \lor $ false, which is false.
Moving to the right side of the expression:
{Z ⊃ [Z ⊃ (Z ⊃ Z)]}
Since Z is false, the conditional statement is true (anything follows from false). 
The expression in the brackets evaluates to true because all Zs are the same and the implication is true when the antecedent is false. 
So, the entire right side of the expression is true. 
Since false ⊃ true is true, the entire expression is true.

Assume A, B, C Are True; X, Y, Z Are ∨ \lor ∨

Assume A, B, C Are True; X, Y, Z Are $\lor$