Write the component statement of the following compound statements and check whether the compound statement is true or false.
(i) 57 is divisible by 2 or 3 .
(ii) 24 is a multiple of 4 and 6.
(ii) All living things have two eyes and two legs.
(iv) 2 is an even number and a prime number.

Explanation

To solve the problem, we need to break down each compound statement into its component statements and then evaluate whether each compound statement is true or false.

### Step-by-step Solution:

**(i) Compound Statement: 57 is divisible by 2 or 3.**

1. **Component Statements:**
- Statement A: 57 is divisible by 2.
- Statement B: 57 is divisible by 3.

2. **Truth Values:**
- Statement A: 57 is not divisible by 2 (False).
- Statement B: 57 is divisible by 3 (True).

3. **Evaluation of Compound Statement:**
- The compound statement uses "or," which means it is true if at least one of the component statements is true. Since Statement B is true, the compound statement is true.

**Conclusion:** The compound statement "57 is divisible by 2 or 3" is **True**.

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**(ii) Compound Statement: 24 is a multiple of 4 and 6.**

1. **Component Statements:**
- Statement A: 24 is a multiple of 4.
- Statement B: 24 is a multiple of 6.

2. **Truth Values:**
- Statement A: 24 is divisible by 4 (True).
- Statement B: 24 is divisible by 6 (True).

3. **Evaluation of Compound Statement:**
- The compound statement uses "and," which means it is true only if both component statements are true. Since both Statement A and Statement B are true, the compound statement is true.

**Conclusion:** The compound statement "24 is a multiple of 4 and 6" is **True**.

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**(iii) Compound Statement: All living things have two eyes and two legs.**

1. **Component Statements:**
- Statement A: All living things have two eyes.
- Statement B: All living things have two legs.

2. **Truth Values:**
- Statement A: This is false because many living things do not have two eyes (e.g., insects).
- Statement B: This is also false because many living things do not have two legs (e.g., snakes, insects).

3. **Evaluation of Compound Statement:**
- The compound statement uses "and," which means it is true only if both component statements are true. Since both Statement A and Statement B are false, the compound statement is false.

**Conclusion:** The compound statement "All living things have two eyes and two legs" is **False**.

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**(iv) Compound Statement: 2 is an even number and a prime number.**

1. **Component Statements:**
- Statement A: 2 is an even number.
- Statement B: 2 is a prime number.

2. **Truth Values:**
- Statement A: 2 is an even number (True).
- Statement B: 2 is a prime number (True).

3. **Evaluation of Compound Statement:**
- The compound statement uses "and," which means it is true only if both component statements are true. Since both Statement A and Statement B are true, the compound statement is true.

**Conclusion:** The compound statement "2 is an even number and a prime number" is **True**.

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### Summary of Results:
1. (i) True
2. (ii) True
3. (iii) False
4. (iv) True

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