MHT CET · Maths · Mathematical Reasoning
Contrapositive of the statement
'If two numbers are not equal, then their squares are not equal', is
- A If the squares of two numbers are not equal, then the numbers are equal.
- B If the squares of two numbers are equal, then the numbers are not equal.
- C If the squares of two numbers are equal, then the numbers are equal.
- D If the squares of two numbers are not equal, then the numbers are not equal.
Answer & Solution
Correct Answer
(C) If the squares of two numbers are equal, then the numbers are equal.
Step-by-step Solution
Detailed explanation
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.
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.
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