Which of the following statements are true? Give a reason to support your answer. (i) For any two sets A and B either A B or B A. (ii) Every subset of an infinite set is infinite. (iii) Every subset of a finite set is finite. (iv) Every set has a proper subset. (v) {a,b,a,b,a,b,….} is an infinite set. (vi) {a,b,c} and {1,2,3} are equivalent sets. (vii) A set can have infinitely many subsets.

Question

Philoid · Accepted Answer

(i) False

No, it is not necessary for any two set A and B to be either A B or B A.

Let A = {1,2} and B ={a,b}

Here neither A B nor B A.

(ii) False

A = {1,2,3} It is subset of infinite set N and is finite.

(iii) True

Even if we think logically then also smaller part of something finite can never be infinite.

(iv) False

Null set or empty set does not have a proper subset.

(v) False

We do not repeat elements in a set, so the given set becomes {a,b} which is a finite set.

(vi) True

In both of the number of the set of elements are same.

(vii) False

In A = {1}

The subsets are ϕ and {1} which are finite.