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

(ii) Every subset of an infinite set is infinite

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Solution

Here, ${0, 1, 2, 3}$ is a finite subset of infinite set $W$ of whole numbers.
So, given statement is false.

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Similar questions

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.

A \subseteq B or B \subseteq A;

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

(vii) A set can have infinitely many subsets.

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

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

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

(iv) Every set has a proper subset

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