Question

If ( K ) and ( L ) are sets and ( n(K)=8, n(L)=14 ), and ( n(K ∩ L)=4 ), find ( n(K ∪ L) ).

Answer 1

To find the number of elements in the union of sets K and L, use the formula n(K ⋃ L) = n(K) + n(L) - n(K ∩ L). Given n(K) = 8, n(L) = 14, and n(K ∩ L) = 4, the result is n(K ⋃ L) = 18.

Step-by-step explanation:

You are asked to find the number of elements in the union of two sets, given the number of elements in each set and their intersection. Recall that the formula for finding the number of elements in the union of two sets K and L is:

n(K ⋃ L) = n(K) + n(L) - n(K ∩ L)

Given that n(K) = 8, n(L) = 14, and their intersection n(K ∩ L) = 4, we can plug these values into the formula:

n(K ⋃ L) = 8 + 14 - 4

n(K ⋃ L) = 22 - 4

n(K ⋃ L) = 18

Therefore, the number of elements in the union of sets K and L is 18.