The conditional statement [((p q) (( p) r)) ((( p) r) (p q))] is :

Question

The conditional statement

$$((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q))$$ is :

Accepted Answer

p
    q
    r
    $$ \sim $$ p
    A =
p $$ \wedge $$ q
    B =
$$ \sim $$ p $$ \vee $$ r
    C =
(A $$ \to $$ B)
    D =
(B $$ \to $$ A)
    C $$ \vee $$ D

T
    T
    T
    F
    T
    T
    T
    T
    T

T
    T
    F
    F
    T
    F
    T
    T
    T

T
    F
    T
    F
    F
    T
    T
    F
    T

T
    F
    F
    F
    F
    F
    T
    T
    T

F
    T
    T
    T
    F
    T
    T
    F
    T

F
    T
    F
    T
    F
    T
    T
    F
    T

F
    F
    T
    T
    F
    T
    T
    F
    T

F
    F
    F
    T
    F
    T
    T
    F
    T

$$\therefore$$ Given statement is a tautology.

Solutions · 1