Explanation:

To determine whether a set is a semigroup, we need to check if the set is closed under an associative binary operation. Additionally, a semigroup does not necessarily require every element to have an inverse.

Let's analyze each option to see if it satisfies the conditions of a semigroup:

a) (Z, *)
- The set of integers (Z) with the operation of multiplication (*).
- This is a semigroup since multiplication is closed on integers and is associative.
- However, this semigroup has inverses for all non-zero elements. For example, the inverse of 2 is 1/2.
- Therefore, option a) is not the correct answer.

b) (N, *)
- The set of natural numbers (N) with the operation of multiplication (*).
- This is not a semigroup since multiplication is not closed on natural numbers. For example, multiplying two natural numbers may result in a non-natural number.
- Therefore, option b) is not the correct answer.

c) (R, +)
- The set of real numbers (R) with the operation of addition (+).
- This is a semigroup since addition is closed on real numbers and is associative.
- However, this semigroup has inverses for all elements. For example, the inverse of 2 is -2.
- Therefore, option c) is not the correct answer.

d) None of these
- This is the correct answer since none of the given options satisfy the conditions of a semigroup with only the identity element having an inverse.
- In a semigroup where only the identity element has an inverse, the operation must be closed and associative, and every non-identity element must not have an inverse.
- None of the given options satisfy these conditions.
- Therefore, option d) is the correct answer.

Conclusion:
The correct answer is option d) None of these because none of the given options satisfy the conditions of a semigroup with only the identity element having an inverse.