Let p be the proposition that Mathematics is interesting and q be the proposition that Mathematics is difficult, then the symbol `p ^^ q` means

Options

A. Mathematics is interesting implies that mathematics is difficult
B. Mathematics is interesting implies and is implied by Mathematics is difficult
C. Mathematics is interesting and Mathematics is difficult
D. Mathematics is intersting or Mathematics is difficult

Answer

To solve the question, we need to interpret the logical symbol `p ∧ q`, where:

- Let \( p \) be the proposition "Mathematics is interesting."
- Let \( q \) be the proposition "Mathematics is difficult."

The symbol `p ∧ q` represents the logical conjunction of \( p \) and \( q \).

### Step-by-Step Solution:

1. **Identify the Propositions**:
- \( p \): Mathematics is interesting.
- \( q \): Mathematics is difficult.

2. **Understand the Symbol**:
- The symbol `∧` (read as "and") represents the logical conjunction. This means that both propositions must be true for the conjunction to be true.

3. **Combine the Propositions**:
- The expression `p ∧ q` means both \( p \) and \( q \) are true simultaneously. Therefore, we can express this as:
- "Mathematics is interesting and Mathematics is difficult."

4. **Final Answer**:
- Thus, the meaning of the symbol `p ∧ q` is: "Mathematics is interesting and Mathematics is difficult."