"If two triangle are congruent, then their areas are equal." Is the given statement, then the contrapositive…

"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)
  1. It two triangles are not congruent. then their areas are equal
  2. If two triangles are not congruent, then their areas are not equal
  3. If areas of two triangles are equal, then they are congruent
  4. If areas of two triangles are not equal, then they arc congruent

Solution

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.

Asked in: MHT CET 2021 (24 Sep Shift 1)

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