Given the following two statements: [( S_1 ):( q p ) ( p q )] is a tautology [( S_2 ): ,, …

Question

Given the following two statements:

$$\left( {{S_1}} \right):\left( {q \vee p} \right) \to \left( {p \leftrightarrow  \sim q} \right)$$ is a tautology

$$\left( {{S_2}} \right):  \,\,\sim q \wedge \left( { \sim p \leftrightarrow q} \right)$$  is a fallacy. Then:

Accepted Answer

Truth table for S1 :

p
    q
    ~q
    $${q \vee p}$$
    $${p \leftrightarrow  \sim q}$$
    $$\left( {q \vee p} \right) \to \left( {p \leftrightarrow  \sim q} \right)$$

T
    T
    F
    T
    F
    F

T
    F
    T
    T
    T
    T

F
    T
    F
    T
    T
    T

F
    F
    T
    F
    F
    T

$$ \therefore $$ S1
 is not correct.

Truth table for S2 :

p
    q
    ~q
    ~p
    $${ \sim p \leftrightarrow q}$$
    $$ \sim q \wedge \left( { \sim p \leftrightarrow q} \right)$$

T
    T
    F
    F
    F
    F

T
    F
    T
    F
    T
    T

F
    T
    F
    T
    T
    F

F
    F
    T
    T
    F
    F

$$ \therefore $$ S2
 is also not correct.

Solutions · 1