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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Solution

Given sets: A={ 1,3,5 } , B={ 2,4,6 } and C={ 0,2,4,6,8 } .

(i)

Given set is { 0,1,2,3,4,5,6 }

The set consisting of elements of set A , set B and set C together is { 0,1,3,5,2,4,6,8 } .

Thus, the given set contains all the elements of the above set except 8 .

Therefore, the set cannot be the universal set for sets A , B and C .

(ii)

Given set is ϕ

The set consisting of elements of set A , set B and set C together is { 0,1,3,5,2,4,6,8 } .

Thus, the given set doesn’t contain any element.

Therefore, the set cannot be the universal set for sets A , B and C .

(iii)

Given set is { 0,1,2,3,4,5,6,7,8,9,10 } .

The set consisting of elements of set A , set B and set C together is { 0,1,3,5,2,4,6,8 } .

Thus, the given set contains all the elements of the above set.

Therefore, the set can be a universal set for sets A , B and C .

(iv)

Given set is { 1,2,3,4,5,6,7,8 } .

The set consisting of elements of set A , set B and set C together is { 0,1,3,5,2,4,6,8 } .

Thus, the given set contains all the elements of the above set except 0.

Therefore, the set cannot be the universal set for sets A , B and C .

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Similar questions

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}

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 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 sets

A, B

and

C

{0, 1, 2, 3, 4, 5, 6}

ii)

ϕ

iii)

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

iv)

{0, 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 universal set for all the three sets A, B and C

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