Mathematical Reasoning Question 12
Question 12 - 01 February - Shift 2
Which of the following statements is a tautology ?
(1) $p \to(p \Lambda(p \to q))$
(2) $(p \Lambda q) \to(\sim(p) \to q))$
(3) $(p \Lambda(p \to q)) \to \sim q$
(4) $p V(p \Lambda q)$
Show Answer
Answer: (2)
Solution:
(i) $p \to(p \Lambda(p \to q))$
$(\sim p) V(p \Lambda(\sim p \vee q))$
$(\sim p) V(f V(p \Lambda q))$
$\sim p V(p \Lambda q)=(\sim p V p) \Lambda(\sim p V q)$
$=\sim pVq$
(ii) $(p \wedge q) \to(\sim p \to q)$
$\sim(p \Lambda q) V(p V q)=t$
${a, b, d} V{a, b, c}=V$
Tautology
(iii) $(p \Lambda(p \to q)) \to \sim q$
$\sim(p \Lambda(\sim p Vq)) V \sim q=\sim(p \Lambda q) V \sim q=\sim p V \sim q$
Not tantology
(iv) $p V(p \Lambda q)=p$
