Check whether the compound statement is true or false. Write
the component statements.
(a) A square is a quadrilateral and its four sides are equal.
(b) “0” is either a positive number or negative number.

Answer

To solve the problem, we need to analyze the two compound statements provided, determine their truth values, and identify their component statements.

### Step-by-step Solution:

**(a)** The first statement is: "A square is a quadrilateral and its four sides are equal."

1. **Identify the component statements:**
- Component Statement 1 (C1): "A square is a quadrilateral."
- Component Statement 2 (C2): "Its four sides are equal."

2. **Evaluate the truth of each component:**
- C1: A square is indeed a quadrilateral (a four-sided figure). This statement is **True**.
- C2: A square has four sides that are equal in length. This statement is also **True**.

3. **Combine the truth values:**
- Since both component statements are true and they are connected by "and," the compound statement is **True**.

**(b)** The second statement is: "0 is either a positive number or a negative number."

1. **Identify the component statements:**
- Component Statement 1 (C1): "0 is a positive number."
- Component Statement 2 (C2): "0 is a negative number."

2. **Evaluate the truth of each component:**
- C1: 0 is not a positive number. This statement is **False**.
- C2: 0 is not a negative number. This statement is also **False**.

3. **Combine the truth values:**
- Since both component statements are false and they are connected by "or," the compound statement is **False** (for an "or" statement to be true, at least one component must be true).

### Final Results:
- For statement (a): The compound statement is **True**.
- For statement (b): The compound statement is **False**.

### Component Statements:
- For statement (a):
- C1: "A square is a quadrilateral." (True)
- C2: "Its four sides are equal." (True)

- For statement (b):
- C1: "0 is a positive number." (False)
- C2: "0 is a negative number." (False)