Write the following compound statements symbolically, assuming the first part of each statement as p and the second part as q :
(1) Inspite of bad weather, India won the cricket match.
(2) A triangles is equilateral if and only if it is equiangular.
(3) Price increases and demand falls.

Answer

To convert the given compound statements into symbolic form using the variables \( p \) and \( q \), we will follow these steps:

### Step 1: Identify the Statements
We have three statements to analyze:
1. "In spite of bad weather, India won the cricket match."
2. "A triangle is equilateral if and only if it is equiangular."
3. "Price increases and demand falls."

### Step 2: Define \( p \) and \( q \)
Assuming:
- \( p \): The first part of each statement.
- \( q \): The second part of each statement.

### Step 3: Symbolically Represent Each Statement

1. **First Statement**: "In spite of bad weather, India won the cricket match."
- Here, we can define:
- \( p \): "Bad weather."
- \( q \): "India won the cricket match."
- The phrase "in spite of" suggests that both conditions are true simultaneously, so we represent this as:
\[ p \land q \]

2. **Second Statement**: "A triangle is equilateral if and only if it is equiangular."
- We can define:
- \( p \): "A triangle is equilateral."
- \( q \): "A triangle is equiangular."
- The phrase "if and only if" indicates a biconditional relationship, so we represent this as:
\[ p \iff q \]

3. **Third Statement**: "Price increases and demand falls."
- We can define:
- \( p \): "Price increases."
- \( q \): "Demand falls."
- The word "and" indicates that both conditions are true simultaneously, so we represent this as:
\[ p \land q \]

### Final Symbolic Representations
1. First Statement: \( p \land q \)
2. Second Statement: \( p \iff q \)
3. Third Statement: \( p \land q \)