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Byju's Answer
Standard XII
Mathematics
Contra-Positive
The contrapos...
Question
The contrapositive of "if in a triangle
A
B
C
,
A
B
=
A
C
, then
∠
B
=
∠
C
", is
A
If in a triangle
A
B
C
,
∠
B
=
∠
C
, then
A
B
=
A
C
.
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B
If in a triangle
A
B
C
,
A
B
≠
A
C
, then
∠
B
≠
∠
C
.
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C
If in a triangle
A
B
C
,
∠
B
≠
∠
C
, then
A
B
≠
A
C
.
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D
If in a triangle
A
B
C
,
∠
B
≠
∠
C
, then
A
B
=
A
C
.
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Solution
The correct option is
C
If in a triangle
A
B
C
,
∠
B
≠
∠
C
, then
A
B
≠
A
C
.
Take
p
:
A
B
=
A
C
and
q
:
∠
B
=
∠
C
So the given statement is symbolically represented as
p
→
q
Now by definition, Contrapositive of a conditional statement
p
→
q
is
∼
q
→
∼
p
∼
q
:
∠
B
≠
∠
C
and
∼
p
:
A
B
≠
A
C
Thus
∼
q
→
∼
p
is given by
If in a
△
A
B
C
,
∠
B
≠
∠
C
then
A
B
≠
A
C
.
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