p: If 7 is an odd number,then 7 is divisible | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The contrapositive of a conditional statement $P \implies Q$ is $
eg Q \implies 
eg P$.For statement $p$: $P$ is '$7$ is an odd number' (True),$

Vedclass · Accepted Answer

$(F, T)$

Vedclass · Answer

(C) The contrapositive of a conditional statement $P \implies Q$ is $
eg Q \implies 
eg P$.For statement $p$: $P$ is '$7$ is an odd number' (True),$Q$ is '$7$ is divisible by $2$' (False). The contrapositive is 'If $7$ is not divisible by $2$,then $7$ is not an odd number'. Since $7$ is not divisible by $2$ (True) and $7$ is an odd number (True),the statement 'If True,then False' is False. Thus,$V_1 = F$.For statement $q$: $P$ is '$7$ is a prime number' (True),$Q$ is '$7$ is an odd number' (True). The contrapositive is 'If $7$ is not an odd number,then $7$ is not a prime number'. Since $7$ is an odd number (True),the antecedent 'If $7$ is not an odd number' is False. $A$ conditional statement with a False antecedent is always True. Thus,$V_2 = T$.Therefore,$(V_1, V_2) = (F, T)$.

$p$: If $7$ is an odd number,then $7$ is divisible by $2$.
$q$: If $7$ is a prime number,then $7$ is an odd number.
If $V_1$ and $V_2$ are the respective truth values of the contrapositive of $p$ and $q$,then $(V_1, V_2) \equiv$

Similar Questions

The negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is:

Consider the following two propositions:
$P_1: \sim( p \rightarrow \sim q )$
$P_2: ( p \wedge \sim q ) \wedge ((\sim p ) \vee q )$
If the proposition $p \rightarrow ((\sim p ) \vee q )$ is evaluated as $FALSE$,then

The given circuit is equivalent to:

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

Write the negation of the following statement:
Every natural number is an integer.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$p$: If $7$ is an odd number,then $7$ is divisible by $2$.$q$: If $7$ is a prime number,then $7$ is an odd number.If $V_1$ and $V_2$ are the respective truth values of the contrapositive of $p$ and $q$,then $(V_1, V_2) \equiv$