Question

If n(G) = 20, n(H) = 30, n(G ⋂ H) = 5, find n(G ⋃ H)
a) 25
b) 40
c) 45
d) 55

Answer 1

The number of elements in the union of sets G and H, denoted n(G ⋃ H), is found using the principle of inclusion-exclusion which results in 45, corresponding to option c).

Step-by-step explanation:

To find n(G ⋃ H), which represents the number of elements in the union of sets G and H, you can use the principle of inclusion-exclusion for sets. This principle states that the number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements that are in both sets.

The formula looks like this: n(G ⋃ H) = n(G) + n(H) - n(G ⋂ H).

Using the values given:

• n(G) = 20
• n(H) = 30
• n(G ⋂ H) = 5

Substituting these into the formula yields:

n(G ⋃ H) = 20 + 30 - 5 = 50 - 5 = 45.

Therefore, the number of elements in the union of sets G and H is 45, which corresponds to option c).