The number of ordered triplets of the truth v | vedclass

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(B) To find the number of ordered triplets $(p, q, r)$ for which the statement $(p \vee q) \wedge (p \vee r) \Rightarrow (q \vee r)$ is True,we constr

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(B) To find the number of ordered triplets $(p, q, r)$ for which the statement $(p \vee q) \wedge (p \vee r) \Rightarrow (q \vee r)$ is True,we construct the truth table:| $p$ | $q$ | $r$ | $p \vee q$ | $p \vee r$ | $(p \vee q) \wedge (p \vee r)$ | $q \vee r$ | $(p \vee q) \wedge (p \vee r) \Rightarrow (q \vee r)$ ||---|---|---|---|---|---|---|---|| $T$ | $T$ | $T$ | $T$ | $T$ | $T$ | $T$ | $T$ || $T$ | $T$ | $F$ | $T$ | $T$ | $T$ | $T$ | $T$ || $T$ | $F$ | $T$ | $T$ | $T$ | $T$ | $T$ | $T$ || $T$ | $F$ | $F$ | $T$ | $T$ | $T$ | $F$ | $F$ || $F$ | $T$ | $T$ | $T$ | $T$ | $T$ | $T$ | $T$ || $F$ | $T$ | $F$ | $T$ | $F$ | $F$ | $T$ | $T$ || $F$ | $F$ | $T$ | $F$ | $T$ | $F$ | $T$ | $T$ || $F$ | $F$ | $F$ | $F$ | $F$ | $F$ | $F$ | $T$ |Counting the rows where the final column is $T$,we find there are $7$ such cases.Thus,the number of ordered triplets is $7$.

The number of ordered triplets of the truth values of $p, q$ and $r$ such that the truth value of the statement $(p \vee q) \wedge (p \vee r) \Rightarrow (q \vee r)$ is True,is equal to

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