Which of the following statement is equivalent to the statement "if `2 + 2 = 4` then India is country" ?

Options

A. `2 + 2 = 4` or India is a country
B. `2 + 2 = 4` and India is a country
C. `2 + 2 != 4` or India is a country
D. `2 + 2 = 4` or India is not a country

Answer

To determine which statement is equivalent to "if \(2 + 2 = 4\) then India is a country," we need to analyze the logical structure of the statement.

### Step 1: Understand the original statement
The original statement can be expressed in logical terms as:
- Let \(P\) be the statement "2 + 2 = 4."
- Let \(Q\) be the statement "India is a country."
- The original statement is then \(P \implies Q\) (if \(P\) then \(Q\)).

### Step 2: Identify the contrapositive
The contrapositive of a statement \(P \implies Q\) is \(\neg Q \implies \neg P\) (if not \(Q\) then not \(P\)). This is logically equivalent to the original statement.
- Here, \(\neg Q\) means "India is not a country."
- \(\neg P\) means "2 + 2 is not equal to 4."
- Thus, the contrapositive is: "If India is not a country, then \(2 + 2\) is not equal to \(4\)."

### Step 3: Evaluate the given options
To find the equivalent statement, we need to check the provided options against the original statement and its contrapositive.

1. **Option A**: "If \(2 + 2 = 4\) and India is a country."
- This does not represent an implication and is not equivalent.

2. **Option B**: "If \(2 + 2 \neq 4\) and India is a country."
- This does not follow the logical structure of the original statement.

3. **Option C**: "If \(2 + 2 \neq 4\), then India is not a country."
- This is the contrapositive and is equivalent to the original statement.

4. **Option D**: "If \(2 + 2 = 4\) and India is not a country."
- This does not represent an implication and is not equivalent.

### Conclusion
The statement that is equivalent to "if \(2 + 2 = 4\) then India is a country" is **Option C**: "If \(2 + 2 \neq 4\), then India is not a country."