For statements p and q,which of the following | vedclass

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(D) $1$. $p \wedge q$ is true only when both $p$ and $q$ are true. Thus,option $A$ is incorrect.$2$. $p \rightarrow q$ is false only when $p$ is true

Vedclass · Accepted Answer

$\sim (p \vee q)$ is true only when both $p$ and $q$ are false.

Vedclass · Answer

(D) $1$. $p \wedge q$ is true only when both $p$ and $q$ are true. Thus,option $A$ is incorrect.$2$. $p \rightarrow q$ is false only when $p$ is true and $q$ is false. Thus,option $B$ is incorrect.$3$. $p \Leftrightarrow q$ is true when both $p$ and $q$ have the same truth value (both true or both false). Thus,option $C$ is incorrect.$4$. $\sim (p \vee q)$ is true only when $(p \vee q)$ is false,which occurs only when both $p$ and $q$ are false. Thus,option $D$ is correct.

For statements $p$ and $q$,which of the following is true?

Similar Questions

Check the validity of the statement given below by the method specified against it.
$q:$ If $n$ is a real number with $n > 3$,then $n^{2} > 9$ (by contradiction method).

Among the two statements:
$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.

Which of the following statement patterns is a tautology?
$S_1 \equiv (\sim q \wedge p) \wedge q$
$S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_3 \equiv (p \wedge q) \wedge (\sim p \vee \sim q)$
$S_4 \equiv (p \wedge q) \rightarrow r$

Which of the following statements is a tautology?

Write the contrapositive and converse of the following statement:
If two lines are parallel,then they do not intersect in the same plane.

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