Question

a. 24. The Venn Diagram below shows the badges: camping, swimming, and first aid. number of boy scouts in a certain troop who have earned the following merit Camping Swimming 10 4 7 2 6 3 5 2 First Aid ​

Answer 1

The answer is below

Explanation:

Let C represent the boy scout with camping badge, S for boy scout with swimming badge and F for boy scout with first aid badge.

a) The number of boy scout with first aid badge = boy scout with all three badges + boy scout with first aid badges alone + boy scout with first aid and swimming badges + boy scout with first aid and camping badges

The number of boy scout with first aid badge = 2 + 5 + 6 + 3 = 16

b) The number of boy scout with camping badge or swimming badge = C ∪ S = 10 + 4 + 2 + 6 + 7 + 3 = 32

c) The number of boy scout with camping badge and first badge = C ∩ F = 6 + 2 = 8

d) The number of boy scout with swimming badge but do not have first aid badge = S ∪ F' = 4 + 7 = 11

e) The number of boy scout without camping badge = C' = 7 + 3 + 5 = 15