If A -1-3-5- B -2-4-6- C -1-4 then which of the following is universal set- A- 0-1-2-3-4-5B- 1-2-3-4-6C- -D- 1-2-3-4-5-6-7-8

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Standard XII

Mathematics

Universal Set

If A =1,3,5, ...

Question

If $A = {1, 3, 5}, B = {2, 4, 6}, C = {1, 4}$ then which of the following is universal set?

{0, 1, 2, 3, 4, 5}

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{1, 2, 3, 4, 6}

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{1, 2, 3, 4, 5, 6, 7, 8}

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ϕ

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Solution

The correct option is D ${1, 2, 3, 4, 5, 6, 7, 8}$
$A = {1, 3, 5}, B = {2, 4, 6}, C = {1, 4}$
A set which contains all elements of set $A$ , $B$ and $C$ is universal set
$∴ 1, 2, 3, 4, 5, 6$ should be in the Universal Set.
Out of all the options only set ${1, 2, 3, 4, 5, 6, 7, 8}$ contains all the required elements/numbers and hence option $(D)$ is correct.

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Similar questions

Q. If

A = {1, 3, 5}, B = {2, 4, 6}, C = {1, 4}

then which of the following is universal set?

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set for all the three sets A, B and C

Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B, and C?

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) $Φ$

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

Q. Given the sets

A = {1, 3, 5}, B = {2, 4, 6}

and

C = {0, 2, 4, 6, 8}

, which of the following may be considered as universal set(s) for all the three

(i) {0, 1, 2, 3, 4, 5, 6}

(i i) ϕ

(i i i) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(i v) {1, 2, 3, 4, 5, 6, 7, 8}

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals set (s) for all the three sets A, B and C

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) Φ

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

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