The binary operation ? is defined as follows Which one of the following is…
2009
The binary operation ? is defined as follows
Which one of the following is equivalent to P∨Q?
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Key identity: From the given truth table, the operator ? is false only when the first input is false and the second input is true, so for any inputs A and B we have A?B = A ∨ ¬B.
Verify by the table: when (A,B) = (T,T) → A?B = T; (T,F) → T; (F,T) → F; (F,F) → T. Thus ? is false only for (F,T).
Use the identity A?B = A ∨ ¬B to evaluate the options. For the expression P?¬Q we get:
P?¬Q = P ∨ ¬(¬Q) = P ∨ Q, which is exactly P ∨ Q.
For the other expressions: ¬Q?¬P = ¬Q ∨ ¬(¬P) = ¬Q ∨ P = P ∨ ¬Q, and ¬P?¬Q = ¬P ∨ ¬(¬Q) = ¬P ∨ Q. Neither equals P ∨ Q.
Conclusion: The expression P?¬Q is equivalent to P ∨ Q.
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