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Let X=\left \{ n\; \epsilon\; N:1\leq n\leq 50 \right \}. If A=\left \{ n\; \epsilon\; X:n\; is\; multiple\; of\; 2 \right \} and B=\left \{ n\; \epsilon\; X:n\; is\; multiple\; of\; 7 \right \}, then the number of elements in the smallest subset of X containing both A and B is
Option: 1 29
Option: 2 45
Option: 3 32
Option: 4 16
 

Answers (1)

best_answer

A = {2, 4, 6, 8, 10, ....., 50}

B = {7, 14, 21, 28, 35, 42, 49}

n(A \cap B) = {14, 28, 42}

Smallest subset of X which has all elements of A and B is the union of A and B

And we know

\\\mathrm{n(A\cup B)=n(A)+n(B)-n(A\cap B)}= 25+7-3=29

Posted by

Ritika Jonwal

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