Write the following implications (p implies q) in the form (`~p vv q`) and write its negation. 'If `Delta ABC` is isosceles then the base angles A and B are equal.'

Answer

To solve the problem, we need to express the implication "If triangle ABC is isosceles, then the base angles A and B are equal" in the form of `~p ∨ q` and then find its negation.

### Step-by-Step Solution:

1. **Identify the Statements:**
- Let \( p \) be the statement: "Triangle ABC is isosceles."
- Let \( q \) be the statement: "The base angles A and B are equal."

2. **Write the Implication:**
- The implication can be represented as \( p \implies q \).

3. **Convert to Disjunction:**
- The implication \( p \implies q \) can be rewritten in the form of disjunction as:
\[ p \implies q \equiv \neg p \lor q \]
- Therefore, we can express it as:
\[ \neg p \lor q \]
- Substituting the statements:
\[ \neg (\text{"Triangle ABC is isosceles"}) \lor (\text{"Base angles A and B are equal"}) \]
- This translates to:
\[ \text{"Triangle ABC is not isosceles"} \lor \text{"Base angles A and B are equal"} \]

4. **Write the Negation:**
- The negation of the disjunction \( \neg p \lor q \) is given by:
\[ \neg(\neg p \lor q) \equiv p \land \neg q \]
- Substituting the statements:
\[ p \land \neg q \]
- This translates to:
\[ \text{"Triangle ABC is isosceles"} \land \text{"Base angles A and B are not equal"} \]

### Final Answers:
- The implication in the form \( \neg p \lor q \) is:
\[ \text{"Triangle ABC is not isosceles"} \lor \text{"Base angles A and B are equal"} \]
- The negation of the implication is:
\[ \text{"Triangle ABC is isosceles"} \land \text{"Base angles A and B are not equal"} \]