Consider the following:
p : Question paper is hard.
q : I will fail in the examination.
Then translate the following sentence into symbols :
If I will not fail in the examination, then question paper is not hard.

Answer

To translate the given sentence into symbols, we will follow these steps:

1. **Identify the Statements**:
- Let \( p \): "Question paper is hard."
- Let \( q \): "I will fail in the examination."

2. **Negate the Statements**:
- "I will not fail in the examination" translates to \( \neg q \) (the negation of \( q \)).
- "Question paper is not hard" translates to \( \neg p \) (the negation of \( p \)).

3. **Formulate the Conditional Statement**:
- The sentence "If I will not fail in the examination, then question paper is not hard" can be expressed as:
- If \( \neg q \) (I will not fail), then \( \neg p \) (the question paper is not hard).

4. **Use the Implication Symbol**:
- The implication "If \( \neg q \), then \( \neg p \)" is represented as:
- \( \neg q \implies \neg p \).

5. **Final Symbolic Representation**:
- Therefore, the complete translation of the sentence into symbols is:
- \( \neg q \implies \neg p \).