Consider the statement p : If a hexagon is regular than all its sides and angles are equal. The contrapositive of statement p is

Options

A. If all sides and angles of a hexagon are not equal then it is not regular
B. If all sides and angles of a hexagon are equal then it is regular
C. If all sides and angles of a hexagon are not equal then it is regular
D. If all sides and angles of a hexagon are equal then it is not regular

Answer

To find the contrapositive of the statement \( p \): "If a hexagon is regular, then all its sides and angles are equal," we can follow these steps:

### Step 1: Identify the components of the statement
The statement \( p \) can be broken down into two parts:
- Hypothesis (or antecedent): \( H \) - "A hexagon is regular."
- Conclusion (or consequent): \( C \) - "All its sides and angles are equal."

### Step 2: Write the conditional statement
The statement can be expressed in a conditional form as:
- \( H \rightarrow C \) (If \( H \), then \( C \))

### Step 3: Formulate the negations
To find the contrapositive, we need to negate both the hypothesis and the conclusion:
- Negation of \( H \) (not \( H \)): "A hexagon is not regular."
- Negation of \( C \) (not \( C \)): "Not all its sides and angles are equal."

### Step 4: Write the contrapositive
The contrapositive of the statement \( H \rightarrow C \) is:
- \( \neg C \rightarrow \neg H \) (If not \( C \), then not \( H \))

In words, this translates to:
- "If a hexagon does not have all its sides and angles equal, then it is not regular."

### Final Statement
Thus, the contrapositive of the statement \( p \) is:
- "If a hexagon is not regular, then all its sides and angles are not equal."