Mathematical Reasoning Question 9

Question 9 - 31 January - Shift 1

$(S 1)(p \Rightarrow q) \vee(p \wedge(\sim q))$ is a tautology

$(S 2)((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)$ is a Contradiction. Then

(1) only (S2) is correct

(2) both (S1) and (S2) are correct

(3) both (S1) and (S2) are wrong

(4) only (S1) is correct

Show Answer

Answer: (2)

Solution:

$\mathbf{p}$ $\mathbf{q}$ $\mathbf{p} \Rightarrow \mathbf{q}$ $\sim \mathbf{q}$ $p \wedge \sim q$ $(p \Rightarrow q) \vee(p \wedge \sim q)$
$T$ $T$ $T$ $F$ $F$ $T$
$T$ $F$ $F$ $T$ $T$ $T$
$F$ $T$ $T$ $F$ $F$ $T$
$F$ $F$ $T$ $T$ $F$ $T$
$\sim \mathbf{p}$ $\sim \mathbf{q}$ $\sim \mathbf{p} \Rightarrow \sim \mathbf{q}$ $\sim \mathbf{p} \vee \mathbf{q}$ $((\sim \mathbf{p}) \Rightarrow(\sim \mathbf{q})) \wedge(\sim \mathbf{p}) \vee$
$F$ $F$ $T$ $T$ $T$
$F$ $T$ $T$ $F$ $F$
$T$ $F$ $F$ $T$ $F$
$T$ $T$ $T$ $T$ $T$