Byju's Answer

Standard XII

Mathematics

Empty Set

Which of the ...

Question

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.

(i i)

and

(i i i)

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(i)

only

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(i)

and

(i i)

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(i)

(i i i)

and

(i i i)

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Solution

The correct option is D $(i)$ only
$(i)$ Empty set is considered as subset of all sets.
$(i i)$ Union of an empty set $ϕ$ with a set $X$ is X.
$(i i i)$ Intersection of an empty set with a set $X$ is an empty set .

Suggest Corrections

Similar questions

Find, which of the following sets are empty:

(i)The set of points of intersection of two parallel lines.

(ii) $A = {x : x \in N a n d 5 < x \leq 6}$

(iii) $B = {x : x^{2} + 4 = 0, x \in N}$

(iv) $C = {e v e n n u m b e r s b e t w e e n 6 & 10}$

(v) $D = {p r i m e n u m b e r s b e t w e e n 7 & 11}$

Note : The set, which has no element in it, is called the empty or null set.

Q. Classify the following sets into empty set, finite set and infinite set. In case of (non-empty) finite sets, mention the cardinal number.
{x | x =4n, n

\in

I and x<10}

Q. Which of the following are examples of empty set?
(i) Set of all even natural numbers divisible by

5

(ii) Set of all even prime numbers.
(iii)

{x : x^{2} - 2 = 0

and

x

is rational

}

(iv)

{x : x

is a natural number,

x < 8

and simultaneously

x > 12

(v)

{x : x

is a point common to any two parallel lines

}

Which of the following are examples of empty set ?

(i) Set of all even numbers divisible by 5.

(ii) Set of all even prime numbers.

(iii) { $x : x^{2} = 0$ and x is rational}.

(iv) {x : x is a natural number, x < 8 and simultaneously x > 12}.

(v) {x : x is a point common to any two parallel lines}.

Q. Which of the following are examples of empty set?
(i) Set of all even natural numbers divisible by 5;
(ii) Set of all even prime numbers;
(iii) {x : x² −2 = 0 and x is rational};
(iv) {x : x is a natural number, x < 8 and simultaneously x > 12};
(v) {x : x is a point common to any two parallel lines}.

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Select...

Which of the following regarding null sets are correct.(i) Empty set is considered as subset of all sets.(ii) Union of an empty set ϕ with a set X is an empty set.(iii) Intersection of an empty set with a set X is X.

The correct option is D (i) only(i) Empty set is considered as subset of all sets.(ii) Union of an empty set ϕ with a set X is X.(iii) Intersection of an empty set with a set X is an empty set .

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.

The correct option is D $(i)$ only
$(i)$ Empty set is considered as subset of all sets.
$(i i)$ Union of an empty set $ϕ$ with a set $X$ is X.
$(i i i)$ Intersection of an empty set with a set $X$ is an empty set .