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.
Last updated on Jun 12, 2025
-> The UGC NET June 2025 exam will be conducted from 25th to 29th June 2025.
-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.
-> The exam is conducted bi-annually - in June and December cycles.
-> The exam comprises two papers - Paper I and Paper II. Paper I consists of 50 questions and Paper II consists of 100 questions.
-> The candidates who are preparing for the exam can check the UGC NET Previous Year Papers and UGC NET Test Series to boost their preparations.