If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?

Given, n X = 40 , n X ∩ Y = 10 and n X ∪ Y = 60 We know that, n X ∪ Y = n X + n Y - n X ∩ Y 60 = 40 + n Y - 10 60 = 30 + n Y n Y = 3 0 Therefore, the set Y has 30 elements.

If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?

Given, n X = 40 , n X ∩ Y = 10 and n X ∪ Y = 60 We know that, n X ∪ Y = n X + n Y - n X ∩ Y 60 = 40 + n Y - 10 60 = 30 + n Y n Y = 3 0 Therefore, the set Y has 30 elements.

Decide, among the following sets, which sets are subsets of one and another: A = x : x ∈ R a n d x s a t i s f y x 2 - 8 x + 12 = 0 , B = 2 , 4 , 6 , C = 2 , 4 , 6 , 8 … , D = 6 .

According to the question we have, A = x : x ∈ R a n d x s a t i s f y x 2 - 8 x + 12 = 0 Let us write set A in roster form, x 2 - 8 x + 12 = 0 x 2 - 6 x - 2 x + 12 = 0 x x - 6 - 2 x - 6 = 0 x - 6 x - 2 = 0 x = 2 , x = 6 ∴ A = 2 , 6 We are given, B = 2 , 4 , 6 , C = 2 , 4 , 6 , 8 , . . . , D = 6 If the elements of set A are present in the set B , then A ⊂ B else it will be A ⊄ B . Therefore, we can write it as D ⊂ A ⊂ B ⊂ C Thus, A ⊂ B , A ⊂ C , B ⊂ C , D ⊂ A , D ⊂ B and D ⊂ C .

If x ∈ A and A ∈ B , then x ∈ B .

Let's take example A = { 1 , 2 } and B = { 1 , { 1 , 2 } , { 3 } } . Now, 2 ∈ { 1 , 2 } and { 1 , 2 } ∈ { { 3 } , 1 , { 1 , 2 } } . ∴ A ⊂ B However, 2 ∉ { { 3 } , 1 , { 1 , 2 } } Therefore, if x ∈ A , A ∈ B , then x may or may not belong to B .