Question

The statements p, q and r have truth values True, False and False respectively. The truth values of a logical statement \([\sim (p∧\sim q)∨(q∨\sim r)]\) and its dual are, respectively.....

• A. True, True
• B. True, False
• C. False, True
• D. False, False

Hint:

Evaluate each connective step by step for the dual too.

Answer 1

The Correct Option is B

Step 1: Simplify the statement first:
$\sim(p\wedge\sim q)=\sim p\vee q$. So $S=\sim p\vee q\vee q\vee\sim r$, which is $\sim p\vee q\vee\sim r$.

Step 2: Evaluate:
$\sim p=F$, $q=F$, $\sim r=T$. So $S=T$.

Step 3: Dual:
$S^d=\sim p\wedge q\wedge\sim r\ $ (using the same simplification). Here $\sim p=F$, so $S^d=F$.

Step 4: Match:
True, False: option (B).

Final Answer:
S is True and S dual is False. \[ \boxed{B} \]