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If A = {x: HCF {x,45} =1} & B = {x = 2k; 1≤ k ≤100} then AB =

Answer»

Correct answer is 53

B = {x = 2k; 1≤ k ≤100}

Thus, x(2,4,6,8,10,...100}

B = {2,4,6,8,10,12,...200}

Thus, n(B)=100

Now, 4= {x: HCF(x,45} = 1}

Thus, multiple of 5 and 3 should not be there

Thus, A = {1,2,4,7,8,11,13,4,...}

Thus, A ∩ B will contain elements in B which are not multiple of 2 and 5, i.e., 10, 20, ... 200

Thus, total 20

And not multiple of 3 and 2 i.e., 6, 12, 18,..., 198

Thus, total 33 - 6 = 27

Thus, n(A ∩ B) = 100-47= 53


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