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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.

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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.

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