The contrapositive of the statement "If I rea | vedclass

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Question

(C) Let $p$ and $q$ be the statements:$p: 	ext{I reach the station in time.}$$q: 	ext{I will catch the train.}$The given statement is of the form $p

Vedclass · Accepted Answer

If $I$ will not catch the train,then $I$ do not reach the station in time.

Vedclass · Answer

(C) Let $p$ and $q$ be the statements:$p: 	ext{I reach the station in time.}$$q: 	ext{I will catch the train.}$The given statement is of the form $p ightarrow q$.The contrapositive of the implication $p ightarrow q$ is defined as $\sim q ightarrow \sim p$.Here,$\sim q$ is "$I$ will not catch the train" and $\sim p$ is "$I$ do not reach the station in time."Therefore,the contrapositive is: "If $I$ will not catch the train,then $I$ do not reach the station in time."This matches option $C$.

The contrapositive of the statement "If $I$ reach the station in time,then $I$ will catch the train" is

Similar Questions

If $p$ and $q$ each have truth value $F$,then the truth values of the statement patterns $(\sim p \vee q) \leftrightarrow \sim(p \wedge q)$ and $\sim p \leftrightarrow (p \rightarrow \sim q)$ respectively are

Statement $-1$: The statement $A \to (B \to A)$ is equivalent to $A \to (A \vee B)$.
Statement $-2$: The statement $\sim [(A \wedge B) \to (\sim A \vee B)]$ is a tautology.

If the inverse of the conditional statement $p \to (\sim q \wedge \sim r)$ is false,then the respective truth values of the statements $p, q,$ and $r$ are:

The statement $(p \wedge (p$ $\rightarrow q) \wedge (q$ $\rightarrow r))$ $\rightarrow r$ is :

If a statement $q$ has truth value $False$ and $(p \wedge q) \leftrightarrow r$ has truth value $True$,then which of the following has truth value $True$?

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