MHT CET · Maths · Mathematical Reasoning
"If two triangle are congruent, then their areas are equal." Is the given statement, then the contrapositive of the inverse of the given statement is
(Where p: Two triangles are congruent, \(\mathrm{q}\) : Their areas are equal)
- A It two triangles are not congruent. then their areas are equal
- B If two triangles are not congruent, then their areas are not equal
- C If areas of two triangles are equal, then they are congruent
- D If areas of two triangles are not equal, then they arc congruent
Answer & Solution
Correct Answer
(C) If areas of two triangles are equal, then they are congruent
Step-by-step Solution
Detailed explanation
Let \(p\) : Two triangles are congruent.
q: Their areas are equal.
Logical form of given statement is \(\mathrm{p} \rightarrow \mathrm{q}\)
Inverse of given statement is \(\sim p \rightarrow \sim q\).
Contrapositive of inverse of given statement is \(\sim(\sim q) \rightarrow \sim(\sim p)\) i.e. \(\mathrm{q} \rightarrow \mathrm{p}\) i.e.
If areas of two triangles are equal, then they are congruent.
q: Their areas are equal.
Logical form of given statement is \(\mathrm{p} \rightarrow \mathrm{q}\)
Inverse of given statement is \(\sim p \rightarrow \sim q\).
Contrapositive of inverse of given statement is \(\sim(\sim q) \rightarrow \sim(\sim p)\) i.e. \(\mathrm{q} \rightarrow \mathrm{p}\) i.e.
If areas of two triangles are equal, then they are congruent.
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