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 "If a hexagon is regular, then all its sides and angles are equal," we will follow these steps:

### Step 1: Identify the components of the statement
The statement can be broken down into two parts:
- Let \( A \) be the statement "a hexagon is regular."
- Let \( B \) be the statement "all its sides and angles are equal."

### Step 2: Write the original statement in implication form
The original statement can be expressed as:
\[ A \implies B \]
This means "If \( A \) is true, then \( B \) is true."

### Step 3: Formulate the contrapositive
The contrapositive of an implication \( A \implies B \) is given by:
\[ \neg B \implies \neg A \]
where \( \neg B \) is the negation of \( B \) and \( \neg A \) is the negation of \( A \).

### Step 4: Negate both parts
Now we need to negate both statements:
- The negation of \( B \) ("all its sides and angles are equal") is "not all sides and angles are equal" or "at least one side or angle is not equal."
- The negation of \( A \) ("a hexagon is regular") is "a hexagon is not regular."

### Step 5: Write the contrapositive statement
Combining these negations, the contrapositive can be expressed as:
"If not all sides and angles of a hexagon are equal, then the hexagon is not regular."

### Final Statement
Thus, the contrapositive of the original statement is:
"If at least one side or angle of a hexagon is not equal, then the hexagon is not regular."