JEE MAIN - Mathematics (2020 - 7th January Evening Slot - No. 11)
Let X = {n $$ \in $$ N : 1 $$ \le $$ n $$ \le $$ 50}. If
A = {n $$ \in $$ X: n is a multiple of 2} and
B = {n $$ \in $$ X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.
A = {n $$ \in $$ X: n is a multiple of 2} and
B = {n $$ \in $$ X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.
Answer
29
Explanation
X = {1, 2, 3, 4, …, 50}
A = {2, 4, 6, 8, …, 50} = 25 elements
B = {7, 14, 21, 28, 35, 42, 49} = 7 elements
Here n(A$$ \cup $$B) = n(A) + n(B) – n(A$$ \cap $$B)
= 25 + 7 – 3 = 29
A = {2, 4, 6, 8, …, 50} = 25 elements
B = {7, 14, 21, 28, 35, 42, 49} = 7 elements
Here n(A$$ \cup $$B) = n(A) + n(B) – n(A$$ \cap $$B)
= 25 + 7 – 3 = 29
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