2) The contrapositive of ”If x∈N,then x is integer and x>0"is-----------------------------------------------------------------------------------------------------------------------------------------

The contrapositive of the statement "If \( x \in \mathbb{N} \), then \( x \) is an integer and \( x > 0 \)" is:

**"If \( x \) is not an integer or \( x \leq 0 \), then \( x \notin \mathbb{N} \)."**

### Explanation:
1. The original statement is of the form "If \( P \), then \( Q \)," where:
   - \( P \): \( x \in \mathbb{N} \) (x belongs to the set of natural numbers)
   - \( Q \): \( x \) is an integer and \( x > 0 \)
  
2. The contrapositive of "If \( P \), then \( Q \)" is "If not \( Q \), then not \( P \)."
   - Not \( Q \): \( x \) is not an integer or \( x \leq 0 \)
   - Not \( P \): \( x \notin \mathbb{N} \) (x does not belong to the set of natural numbers)

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### Further Questions:
1. What is the difference between the contrapositive, converse, and inverse of a statement?
2. How do you prove that the contrapositive of a statement is logically equivalent to the original statement?
3. What are some examples of contrapositive statements in real-life scenarios?
4. How does the concept of contrapositive help in mathematical proofs, especially in proving implications?
5. Can you explain the role of contrapositive in logical reasoning and decision-making processes?

### Tip:
When constructing the contrapositive, remember that you negate both parts of the statement and reverse the direction of the implication.

Explore the concept of contrapositive in set theory and logical implications. Learn the contrapositive of the statement 'If x is a natural number, then x is an integer and x > 0'. This detailed explanation covers set theory concepts and logical reasoning.

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