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Let X=n∈N:1≤n≤50. If A=n∈X:n is a multiple of 2 and B=n∈X:n is a multiple of 7. Then the number of elements in the smallest subset of X containing both A and B is _____

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answer is 29.

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Detailed Solution

We have AA=2,4,6,8........50, B=7,14,21,28,35,42,49 and A∩B=14,28,42Also the smallest subset containing both A and B is A∪B∴nA∪B=nA+nB−nA∩B= 25 + 7 – 3 = 29

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Let X=n∈N:1≤n≤50. If A=n∈X:n is a multiple of 2 and B=n∈X:n is a multiple of 7. Then the number of elements in the smallest subset of X containing both A and B is _____