Contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is

Contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is
  1. If the squares of two numbers are not equal, then the numbers are equal.
  2. If the squares of two numbers are equal, then the numbers are not equal.
  3. If the squares of two numbers are equal, then the numbers are equal.
  4. If the squares of two numbers are not equal, then the numbers are not equal.

Solution

Let p : two numbers are not equal. q : squares of two numbers are not equal. Given statement is $\mathrm{p} \rightarrow \mathrm{q}$. $\therefore \quad$ Contrapositive is $\sim \mathrm{q} \rightarrow \sim \mathrm{p}$. i.e., If squares of two numbers are equal, then the numbers are equal.

Asked in: MHT CET 2024 (11 May Shift 2)

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