Which statement is a converse statement of the conditional statement below.If the rock is big, then the rock is heavy.A. If the rock is not heavy, then the rock is not big.B. If the rock is heavy, then the rock is big.C. If the rock is not big, then the rock is not heavy. D. The rock is heavy if and only if the rock is big.2.  Which statement is an inverse statement of the conditional statement below.If it is summer, then the temperature is hot.A. If the temperature is hot, then it is summer.B. The temperature is hot if and only if it is summer.C. If the temperature is not hot, then it is not summer. D. If it is not summer, then the temperature is not hot.3.  Which statement is the contrapositive statement of the conditional statement below.If a number is even, then it is divisible by 2.The contrapositiveisSelect○ If a number is divisible by 2, then it is even.○ If a number is not even, then it is not divisible by 2.○ If a number is not divisible by 2, then it is not even.

Let's analyze each question in detail.

### 1. Converse Statement
A **converse** of a conditional statement is formed by switching the hypothesis and conclusion.

- **Given statement**: "If the rock is big, then the rock is heavy."
- **Converse**: "If the rock is heavy, then the rock is big."

So, the correct answer is:
**B. If the rock is heavy, then the rock is big.**

### 2. Inverse Statement
An **inverse** of a conditional statement is formed by negating both the hypothesis and the conclusion.

- **Given statement**: "If it is summer, then the temperature is hot."
- **Inverse**: "If it is not summer, then the temperature is not hot."

So, the correct answer is:
**D. If it is not summer, then the temperature is not hot.**

### 3. Contrapositive Statement
A **contrapositive** of a conditional statement is formed by switching and negating both the hypothesis and the conclusion.

- **Given statement**: "If a number is even, then it is divisible by 2."
- **Contrapositive**: "If a number is not divisible by 2, then it is not even."

So, the correct answer is:
**○ If a number is not divisible by 2, then it is not even.**

Would you like any more details on these concepts, or do you have any questions?

Here are five related questions to expand your understanding:

1. What is the definition of a biconditional statement?
2. How do you determine if a conditional statement is logically equivalent to its converse?
3. What is the difference between an inverse and a contrapositive?
4. Can the contrapositive of a statement ever be false if the original statement is true?
5. What is an example of a real-life situation where you can use a contrapositive statement?

**Tip:** Remember that a statement and its contrapositive are always logically equivalent, meaning if one is true, the other must be true as well.

Explore the concepts of converse, inverse, and contrapositive statements in logic with detailed explanations and examples. Learn how these concepts apply to conditional statements and their logical equivalents. Suitable for general knowledge seekers and students interested in logical reasoning.

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