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

If $P \Rightarrow (q \vee r)$ is false,then the truth values of $p, q, r$ are respectively

Which of the following is a contradiction?

If truth values of statements $p, q$ are true,and $r, s$ are false,then the truth values of the following statement patterns are respectively:
$a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$
$b: (\sim q \wedge \sim r) \leftrightarrow(p \vee s)$
$c: (\sim p \vee q) \rightarrow(r \wedge \sim s)$

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
Students can take French or Sanskrit as their third language.

Negation of "Paris is in France and London is in England" is

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 $(V_1, V_2) \equiv$