Consider a family with a mother father and three children Le

Consider a family with a mother, father, and three children. Let A1 = {mother has influenza}, A2 = {father has influenza}, A3 = {first child has influenza}, A4 = {second child has influenza}, A5 = {third child has influenza}, B1 = {at least one child has influenza}, B2 = {at least two children has influenza}, C = {at least one parent has influenza}, and D = {at least one person in the family has influenza}.

What does A1 A2 mean?

What does A1 A2 mean?

Are A3, A4, and A5 mutually exclusive? Why?

What does A3 B1 mean?

What does A4 B2 mean?

Express C in terms of A1~A5.

Express D in terms of B1, B2, and C.

Represent C^c in terms of A1~A5.

Represent D^c in terms of B1, B2, and C.

Solution

note : we are suppose to answer till 4 subparts of any question, for rest repost the question again.

a) A1 U A2 = It means clubbing together two groups, in this it will mean both parents have inflenza.

b)A1 A2 mean the common part between the two group, in this there is no common part.

c) A3, A4, and A5 mutually exclusive, yes they are exclusive because they dont have any common part.

d)A3 B1 mean that both will be a part together in this A1 will become a subset of B1