Let A and B be two sets such that n(A) = 52, n(B) = 60 and n(A ∩ B) = 16. Draw a Venn diagram and find :

(i) n(A ∪ B)

(ii) n(A - B)

(iii) n(B - A)

Given:

n(A) = 52

n(B) = 60

n(A ∩ B) = 16

(i) n(A ∪ B)

The number of elements in the union of two sets is found using the formula:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Substituting the values in above, we get:

n(A ∪ B) = 52 + 60 - 16

n(A ∪ B) = 112 - 16

∴ n(A ∪ B) = 96

(ii) n(A - B)

The number of elements that belong to A but not to B is found by subtracting the intersection from n(A):

n(A - B) = n(A) - n(A ∩ B)

Substituting the values in above, we get:

n(A - B) = 52 - 16

∴ n(A - B) = 36

(iii) n(B - A)

The number of elements that belong to B but not to A is found by subtracting the intersection from n(B):

n(B - A) = n(B) - n(A ∩ B)

Substituting the values in above, we get:

n(B - A) = 60 - 16

∴ n(B - A) = 44