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

Options

A. If the squares of two numbers are 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 not equal, then the numbers are equal
D. If the squares of two numbers are not equal, then the numbers are not equal.

Answer

To find the contrapositive of the statement "If two numbers are not equal, then their squares are not equal," we can follow these steps:

### Step 1: Identify the components of the statement
The statement can be expressed in the form "If P, then Q," where:
- P: "Two numbers are not equal."
- Q: "Their squares are not equal."

### Step 2: Negate both parts
To form the contrapositive, we need to negate both P and Q:
- Negation of Q: "Their squares are equal."
- Negation of P: "The two numbers are equal."

### Step 3: Formulate the contrapositive
The contrapositive of the statement "If P, then Q" is "If not Q, then not P." Therefore, we can write:
- Contrapositive: "If the squares of two numbers are equal, then the two numbers are equal."

### Final Answer
The contrapositive of the statement "If two numbers are not equal, then their squares are not equal" is:
**"If the squares of two numbers are equal, then the two numbers are equal."**

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