Let X = n ∈ N : 1 ≤ n ≤ 50 . If A = n ∈ X :   n  i s  a  m u l t i p l e  o f   2 and B = n ∈ X :   n  i s  a  m u l t i p l e  o f  7 , then the numb

Question

Let X = n &#8712; N : 1 &#8804; n &#8804; 50 . If A = n &#8712; X : &#160; n&#160; i s&#160; a&#160; m u l t i p l e&#160; o f &#160; 2 and B = n &#8712; X : &#160; n&#160; i s&#160; a&#160; m u l t i p l e&#160; o f&#160; 7 , then the number of elements in the smallest subset of X , containing both A and B , is.

Quantrex Academy · Accepted Answer

Correct answer: 29

Here, A = 2 , 4 , 6 , . . . . 50 and B = 7 , 14 , . . . 49 Required smallest subset is A &#8746; B . So, n A &#8746; B = n A + n B - n A &#8745; B = 25 + 7 - 3 = 29 .

Let X = n ∈ N : 1 ≤ n ≤ 50 . If A = n ∈ X :   n  i s  a  m u l t i p l e  o f   2 and B = n ∈ X :   n  i s  a  m u l t i p l e  o f  7 , then the number of elements in the smallest subset of X , containing both A and B , is.

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