Write each of the implications `(p implies q)` in the form `(~p vv q)` and hence write the negation of each statement:
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 \( p \implies q \) in the form \( \neg p \lor q \) and then find the negation of the statement.

Let's break it down step by step:

### Step 1: Identify the statements
Let:
- \( p \): "Triangle ABC is isosceles."
- \( q \): "The base angles A and B are equal."

### Step 2: Write the implication
The implication \( p \implies q \) can be rewritten in the form \( \neg p \lor q \):
\[ p \implies q \equiv \neg p \lor q \]

### Step 3: Substitute the statements into the implication
Substituting the identified statements into the implication:
\[ \text{"If triangle ABC is isosceles, then the base angles A and B are equal."} \equiv \neg (\text{"Triangle ABC is isosceles"}) \lor (\text{"The base angles A and B are equal."}) \]
This translates to:
\[ \text{"Triangle ABC is not isosceles or the base angles A and B are equal."} \]

### Step 4: Negate the implication
To find the negation of the implication \( p \implies q \), we negate the expression \( \neg p \lor q \):
\[ \neg(\neg p \lor q) \]

### Step 5: Apply De Morgan's Law
Using De Morgan's Law, we can rewrite the negation:
\[ \neg(\neg p \lor q) \equiv p \land \neg q \]

### Step 6: Substitute back the statements
Now, substituting back the statements:
\[ p \land \neg q \equiv \text{"Triangle ABC is isosceles and the base angles A and B are not equal."} \]

### Final Statement
Thus, the negation of the original statement is:
\[ \text{"Triangle ABC is isosceles and the base angles A and B are not equal."} \]