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The contrapos...
Question
The contrapositive of the statement "If p, then q", is
A
If ~q, then ~p
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B
If p, then ~q
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C
If q, then p
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D
If ~p, then ~q
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Solution
The correct option is
A
If ~q, then ~p
Given statement: "If p, then q"
i.e.,
p
→
q
Contrapositive of
p
→
q
is given by
~q
→
~p and both conveys same meaning.
~q
→
~p is equivalent to: If ~q, then ~p
∴
Option (C) is correct.
Suggest Corrections
2
Similar questions
Q.
Mark the correct answer in each of the following:
The contrapositive of the statement "If p, then q", is
(a) If q, then p
(b) If p, then ~ q
(c) If ~ q, then ~ p
(d) If ~ p, then ~ q
Q.
The contrapositive of the statement p ⇒ ∼q is ________________________.
Q.
Assertion :The contrapositive and converse of the statement: "If
x
is a prime number, then
x
is odd" are:
Contrapositive: "If
x
is not odd, then
x
is not a prime number.
Converse: If
x
is odd, then
x
is a prime number. Reason: If statement
p
implies
q
, then its contrapositive is
∼
q
implies
∼
p
, and its converse is
q
implies
p
.
Q.
STATEMENT 1: The contrapositive of the statement "If you have
6
ice-creams, then you can eat in
6
!
ways" is "If you cannot eat in
6
!
ways, then you do not have
6
ice-creams".
STATEMENT 2: Statement
p
⇒
q
and its contrapositive are not logically equivalent.
Q.
The contrapositive of the statement
p
⟹
∼
q
is
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