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Definition of Sets

State, whethe...

Question

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

(iv) Every set has a proper subset

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Solution

$∵$ Null set or empty set does not have a proper

subset.

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.

Q. 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.

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

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

(vii) A set can have infinitely many subsets.

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Definition of Sets

Standard XII Mathematics

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