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 original statement and the given options.

### Step-by-Step Solution:

1. **Understanding the Original Statement**:
The statement "if \(2 + 2 = 4\) then India is a country" can be expressed in logical terms as \(P \rightarrow Q\), where:
- \(P\) is the statement \(2 + 2 = 4\)
- \(Q\) is the statement "India is a country"

2. **Identifying the Contrapositive**:
The contrapositive of the statement \(P \rightarrow Q\) is \(\neg Q \rightarrow \neg P\), which means "if India is not a country, then \(2 + 2 \neq 4\)". However, we are looking for equivalent statements among the options provided.

3. **Analyzing the Options**:
We will evaluate each option to see if it logically aligns with the original statement.

- **Option 1**: \(2 + 2 = 4 \lor \text{India is a country}\)
- This means either \(2 + 2 = 4\) is true or India is a country. This does not capture the conditional nature of the original statement, so it is incorrect.

- **Option 2**: \(2 + 2 = 4 \land \text{India is a country}\)
- This states that both \(2 + 2 = 4\) and India is a country are true. This is a conjunction and does not reflect the conditional relationship, so it is incorrect.

- **Option 3**: \(2 + 2 \neq 4 \lor \text{India is a country}\)
- This means either \(2 + 2\) is not equal to \(4\) or India is a country. This aligns with the contrapositive logic because if \(2 + 2\) is not equal to \(4\), it does not contradict the original statement, making this option correct.

- **Option 4**: \(2 + 2 = 4 \lor \text{India is not a country}\)
- This suggests either \(2 + 2 = 4\) is true or India is not a country. This does not logically follow from the original statement, so it is incorrect.

4. **Conclusion**:
After evaluating all options, we find that the correct equivalent statement is **Option 3**: \(2 + 2 \neq 4 \lor \text{India is a country}\).