If the truth value of the Boolean expression [( ( p q ) ( q r ) ( r ) ) ( p q )] is false,…

Question

If the truth value of the Boolean expression $$\left( {\left( {p \vee q} \right) \wedge \left( {q \to r} \right) \wedge \left( { \sim r} \right)} \right) \to \left( {p \wedge q} \right)$$ is false, then the truth values of the statements p, q, r respectively can be :

Accepted Answer

p
    q
    r
    $$\underbrace {p \vee q}_a$$
    $$\underbrace {q \to r}_b$$
    $${a \wedge b}$$
    $${ \sim r}$$
    $$\underbrace {a \wedge b \wedge ( \sim r)}_c$$
    $$\underbrace {p \wedge q}_d$$
    $$c \to d$$

T
    F
    T
    T
    T
    T
    F
    F
    F
    T

F
    F
    T
    F
    T
    F
    F
    F
    F
    T

T
    F
    F
    T
    T
    T
    T
    T
    F
    F

F
    T
    F
    T
    F
    F
    T
    F
    F
    T

Solutions · 1