The contrapositive of the statement ` "if 2^(2) =5` then I get first class is

Options

A. if I do not get a first class, then ` 2^(2) =5`
B. if I do not get a first class , then ` 2^(2) ne 5`
C. If I get first class, then `2^(2) =5`
D. none of these

Explanation

To find the contrapositive of the statement "If \(2^2 = 5\), then I get first class," we can follow these steps:

### Step 1: Identify the components of the statement
The given statement can be broken down into two parts:
- Let \(P\) be the statement \(2^2 = 5\).
- Let \(Q\) be the statement "I get first class."

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

### Step 3: Formulate the contrapositive
The contrapositive of an implication \(P \implies Q\) is given by:
\[ \neg Q \implies \neg P \]
This means "If \(Q\) is not true, then \(P\) is not true."

### Step 4: Negate the statements
Now we need to negate both statements:
- The negation of \(Q\) ("I get first class") is "I do not get first class."
- The negation of \(P\) ("\(2^2 = 5\)") is "\(2^2 \neq 5\)."

### Step 5: Write the contrapositive statement
Putting it all together, the contrapositive of the original statement is:
"If I do not get first class, then \(2^2 \neq 5\)."

### Final Answer
The contrapositive of the statement "If \(2^2 = 5\), then I get first class" is:
"If I do not get first class, then \(2^2 \neq 5\)."

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