Classify the following sets as empty, singleton, finite or infinite sets:

(a) A = { }

(b) B = {50}

(c) C = {1, 4, 9, 16, 25}

(d) D = {x : x is a natural number greater than 20}

(e) E = {x : x is a negative whole number}

(a) A = { } has no elements, so it is an empty set.

(b) B = {50} has exactly one element, so it is a singleton set.

(c) C = {1, 4, 9, 16, 25} has 5 elements (a countable number), so it is a finite set.

(d) D = {x : x is a natural number greater than 20} is 21, 22, 23, … which never ends, so it is an infinite set.

(e) E = {x : x is a negative whole number} — whole numbers are 0, 1, 2, 3, …, so there is no negative whole number. Hence E is an empty set.

Hence, (a) Empty set, (b) Singleton set, (c) Finite set, (d) Infinite set and (e) Empty set.