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Standard XII

Mathematics

Cardinal Number

Fill in the b...

Question

Fill in the blanks:

(iii) The empty set is a _______ of every set.

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Solution

Step : Fill in the blanks

If each element of set X is also present in set Y, then set X is said to be the subset of set Y.

Empty set does not have any element in it.

Hence, the empty set is a $s u b s e t - ----- -$ of every set.

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Similar questions

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.

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. An Empty Set

(\emptyset)

is a subset of every set.

if empty set is a subset of every set as it is emty then why when contained within brackets the set is non-empty i.e. if it is empty then how can that set be a set?

Q. Which of the following regarding null sets are correct.

(i)

Empty set is considered as subset of all sets.

(i i)

Union of an empty set

ϕ

with a set

X

is an empty set.

(i i i)

Intersection of an empty set with a set

X

is X.

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Cardinal Number

Standard XII Mathematics

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Fill in the blanks: (iii) The empty set is a _______ of every set.

Step : Fill in the blanks If each element of set X is also present in set Y, then set X is said to be the subset of set Y. Empty set does not have any element in it. Hence, the empty set is a subset––––––– of every set.

Fill in the blanks:

(iii) The empty set is a _______ of every set.

Step : Fill in the blanks

If each element of set X is also present in set Y, then set X is said to be the subset of set Y.

Empty set does not have any element in it.

Hence, the empty set is a $s u b s e t - ----- -$ of every set.