Let p: Maths is intersting and q : Maths is easy, then `p rArr (~p vv q)` is equivalent to

Options

A. It Maths is easy then it is interesting
B. Either Maths is interesting or it easy
C. If Maths is interseting then it is easy
D. Maths is neither interesting nor easy

Answer

To solve the problem, we need to analyze the logical statement given: \( p \Rightarrow (\neg p \lor q) \).

### Step-by-Step Solution:

1. **Identify the Statements**:
- Let \( p \) represent "Maths is interesting".
- Let \( q \) represent "Maths is easy".

2. **Rewrite the Implication**:
- The implication \( p \Rightarrow (\neg p \lor q) \) can be rewritten using the definition of implication. The statement \( p \Rightarrow r \) is equivalent to \( \neg p \lor r \).
- Therefore, we can rewrite \( p \Rightarrow (\neg p \lor q) \) as:
\[ \neg p \lor (\neg p \lor q) \]

3. **Apply Associative Law**:
- By the associative law of disjunction, we can simplify:
\[ \neg p \lor \neg p \lor q = \neg p \lor q \]

4. **Interpret the Result**:
- The expression \( \neg p \lor q \) can be interpreted as "Either Maths is not interesting or Maths is easy".

5. **Conclusion**:
- Thus, the statement \( p \Rightarrow (\neg p \lor q) \) is equivalent to \( \neg p \lor q \).

### Final Answer:
The equivalent statement is \( \neg p \lor q \).

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