Sets, Relations & Functions
Logic and Statements
Grade 11
Question:
<p>If \(p\), \(q\) and \(r\) are simple propositions with truth value true, false and true respectively, then the truth value of \(((\sim p \lor q) \land \sim r) \Rightarrow p\)</p>
<p>(a) true</p>
<p>(b) false</p>
<p>(c) true, if \(r\) is false</p>
<p>(d) true, if \(q\) is true</p>
Step-by-Step Solution
Key Concept: A conditional statement with a false antecedent is always true.
<p>Given: \(p = T\), \(q = F\), \(r = T\).</p><p>We need to find the truth value of \(((\sim p \lor q) \land \sim r) \Rightarrow p\).</p><p>Step 1: \(\sim p = F\), \(\sim r = F\).</p><p>Step 2: \(\sim p \lor q = F \lor F = F\).</p><p>Step 3: \((\sim p \lor q) \land \sim r = F \land F = F\).</p><p>Step 4: \(((\sim p \lor q) \land \sim r) \Rightarrow p = F \Rightarrow T = T\).</p><p>∴ Answer is (a) true.</p>
Correct Answer: A