State, whether the following statement is true? Give reason to support your answer.

(vii) A set can have infinitely many subsets.

Open in App

Solution

Given statement : A set can have infinitely many subsets.

Let, Set $A = {1, 2}$

Subsets of $A$ are ${1}, {2}, {1, 2}, ϕ$ which are finite.

Hence, given statement is false.

Suggest Corrections

Similar questions

A \subseteq B or B \subseteq A;

Which of the following statements are true ? Give reason to support your answer.

(i) For any two sets A and B either A $\subseteq$ B or B $\subseteq$ 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.

State, whether the following statement is true? Give reason to support your answer.

(ii) Every subset of an infinite set is infinite

State, whether the following statement is true? Give reason to support your answer.

(iv) Every set has a proper subset

State, whether the following statement is true? Give reason to support your answer.

(iii) Every subset of a finite set is finite.

Join BYJU'S Learning Program