Which set of numbers could be the universal set for the sets given bel

1.	Which set of numbers could be the universal set for the sets given below? i. A = set of multiples of 5, B = set of multiples of 7, C = set of multiples of 12 ii. P = set of integers which are multiples of 4. T = set of all even square numbers.
Answer» i. A = set of multiples of 5 ∴ A = {5, 10, 15, …} B = set of multiples of 7 ∴ B = {7, 14, 21,…} C = set of multiples of 12 ∴ C = {12, 24, 36, …} Now, set of natural numbers, whole numbers, integers, rational numbers are as follows: N = {1, 2, 3, …}, W = {0, 1, 2, 3, …} I = {…,-3, -2, -1, 0, 1, 2, 3, …} Q = {(p/q) \| p,q ∈ I,q ≠ 0} Since, set A, B and C are the subsets of sets N, W , I and Q. ∴ For set A, B and C we can take any one of the set from N, W, I or Q as universal set. ii. P = set of integers which are multiples of 4. P = {4, 8, 12,…} T = set of all even square numbers T = {2², 4², 6², …} Since, set P and T are the subsets of sets N, W, I and Q. ∴ For set P and T we can take any one of the set from N, W, I or Q as universal set.

Which set of numbers could be the universal set for the sets given below? i. A = set of multiples of 5, B = set of multiples of 7, C = set of multiples of 12 ii. P = set of integers which are multiples of 4. T = set of all even square numbers.

Answer»

i. A = set of multiples of 5

∴ A = {5, 10, 15, …}

B = set of multiples of 7

∴ B = {7, 14, 21,…}

C = set of multiples of 12

∴ C = {12, 24, 36, …}

Now, set of natural numbers, whole numbers, integers, rational numbers are as follows:

N = {1, 2, 3, …}, W = {0, 1, 2, 3, …}

I = {…,-3, -2, -1, 0, 1, 2, 3, …}

Q = {(p/q) | p,q ∈ I,q ≠ 0}

Since, set A, B and C are the subsets of sets N, W , I and Q.

∴ For set A, B and C we can take any one of the set from N, W, I or Q as universal set.

ii. P = set of integers which are multiples of 4.

P = {4, 8, 12,…}

T = set of all even square numbers

T = {2², 4², 6², …}

Since, set P and T are the subsets of sets N, W, I and Q.

∴ For set P and T we can take any one of the set from N, W, I or Q as universal set.