Final answer:
Among the sets provided, the only finite set is d) ∅ (Empty set), as it contains no elements. The sets a) N, b) {Z, N, C, Q}, and c) Z are all infinite, while the notation e) [Z] is not standard and requires clarification.
Step-by-step explanation:
The question involves determining which of the given sets are finite. A finite set is one that has a limited number of elements, which means you can count its elements, and the counting will end.
- a) ℕ (N) - This set represents the set of all natural numbers which is infinite because you can count forever and will never reach the end.
- b) {Z,N,C,Q} - This set refers to several other sets: Z (integers), N (natural numbers), C (complex numbers), and Q (rational numbers). All of these sets are individually infinite.
- c) Z - The set of all integers is also infinite; you can keep counting both in the positive and negative direction without end.
- d) ∅ (Empty set) - The empty set has no elements, which makes it finite by definition.
- e) [Z] - This notation can be interpreted in different ways, but it commonly means the set containing the single element Z. If Z is intended to represent the integers as a single entity, then this would be a finite set containing one element. However, as it's not standard notation, clarification would be needed to provide a definitive answer.
From the options given and the standard understanding of set notation, we can determine that d) ∅ (Empty set) is the only finite set in the list.