Question

Which of the following statement(s) is/are true?
(A) Every subset of an infinite set is infinite.
(B) Every set has a proper subset.
(C) Number of subsets of every set is even.
(D) Every subset of a finite set is finite.

• A. A and B
• B. A, B, and C
• C. B, C, and D
• D. D

Answer 1

Answer: (D)

(a) Is false since the set $N$ of all natural numbers is an infinite set having a finite subset, i.e., $\{1\}$
(b) Is false since $\varnothing$ has no proper subsets.
(c) Is false since number of subsets of an empty set is odd (i.e., $2^{\circ }=1$ ).
(d) Is clearly true.