Question
Download Solution PDFLet P, Q, R and S be Propositions. Assume that the equivalences \(P\leftrightarrow(Q \vee \;\neg\; Q)\) and \(Q \leftrightarrow R\) hold. Then the truth value of the formula \(\left( {P \wedge Q} \right) \Rightarrow \left( {\left( {P \wedge R} \right) \vee S} \right)\) is always:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 1.
Key Points
Equivalence condition (Both RHS and LHS should be True)= P⇔(QV¬Q)
Holding condition (Both RHS and LHS may True/False)=Q⇔R
Step 1: (P∧Q)⇒((P∧R)VS)[Note: Q, R, and S is True]
| P | Q | R | S | (P∧Q) | ((P∧R)VS) | (P∧Q)⇒((P∧R)VS) |
| T | T | T | T | T | T | T |
Note: The given condition is True
Step-2:(P∧Q)⇒((P∧R)VS) [Note: Q, R, and S is False]
| P | Q | R | S | (P∧Q) | ((P∧R)VS) | (P∧Q)⇒((P∧R)VS) |
| T | F | F | F | F | F | T |
Note: The given condition is True
Hence the correct answer is True.
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