p : If end digit of an integer is 5 then end digit of its square is also 5.
Statement p is same as the

Options

A. If end digit of square of an integer is not 5, then. end of digit of integer is not 5
B. If end digit of a number is not 5, then we cannot say anything about the end digit of that integer
C. The end digit of an integer is 5 only if square of' its end digit is 5.
D. All of these·

Answer

To solve the problem, we need to analyze the statement \( p \): "If the end digit of an integer is 5, then the end digit of its square is also 5." We will explore the options provided to determine which statement is logically equivalent to \( p \).

### Step-by-Step Solution:

1. **Understanding the Statement \( p \)**:
- The statement \( p \) can be expressed in logical terms as:
\[ p: \text{If } A \text{ (the end digit of an integer is 5), then } B \text{ (the end digit of its square is also 5).} \]

2. **Identifying the Contrapositive**:
- The contrapositive of a statement \( p \) is logically equivalent to the original statement. The contrapositive of \( p \) is:
\[ \text{If } \neg B \text{ (the end digit of the square is not 5), then } \neg A \text{ (the end digit of the integer is not 5).} \]
- This means that if the square does not end in 5, then the original integer cannot end in 5 either.

3. **Evaluating the Options**:
- **Option A**: "If the end digit of the square is not 5, then the end digit of the integer is not 5."
- This is the contrapositive of \( p \) and is therefore logically equivalent to \( p \).
- **Option B**: "If the end digit of the integer is not 5, then we cannot conclude anything about the end digit of its square."
- This is the inverse of \( p \) and is not necessarily true.
- **Option C**: "The end digit of an integer is 5 only when the end digit of its square is 5."
- This is a direct statement and does not hold true in all cases.
- **Option D**: "Both A and C are true."
- Since only A is logically equivalent to \( p \), this option is incorrect.

4. **Conclusion**:
- The statement that is logically equivalent to \( p \) is **Option A**.

### Final Answer:
The statement \( p \) is the same as **Option A**.