Verified Solution • 2025–26 Session
moderate
QJEEM20Maa41b: JEE Main 2020 Mathematics - Class 11 JEEM20Maa41b Solution: Let X = {n ∈ N : 1 ≤ n ≤ 50}. If A = {n ∈ X: n is a multiple of …
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 ________.
A = {n
B = {n
Step-by-Step Verified Solution
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 B) = n(A) + n(B) – n(A 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
= 25 + 7 – 3 = 29