Question

Let A, B and C be events of a sample space. Complete the following table.

Events	Description
(A & B)	Both A and B occur
	At least one of A and B occur
(A & (not B))
	Neither A nor B occur
( A or B or C
	All three A, B and C occur
	Exactly one of A, B and C occur
	Exactly two of A, B and C occur
	At most one of A, B and C occur

Short answer

Table:

Events	Description
(A & B)	Both A and B occur
(A or B)	At least one of A and B occur
(A & (not B))	A occur but B does not occur
not( A or B)	Neither A nor B occur
( A or B or C)	At least one of A, B and C occur
(A & B & C)	All three A, B and C occur
(A & not B & not C) or (B & not A & not C) or (C & not B & not A)	Exactly one of A, B and C occur
(A & not B & not C) or (B & not A & not C) or (C & not B & not A)	Exactly two of A, B and C occur
(A & not B & not C) or (B & not A & not C) or (C & not B & not A)	At most one of A, B and C occurs

Step-by-step solution

Step 1. Given information. 

Allow events A, B, and C to be sample space events.

Step 2. Complete the given table: 

Events	Description
(A & B)	Both A and B occur
(A or B)	At least one of A and B occur
(A & (not B))	A occur but B does not occur
not( A or B)	Neither A nor B occur
( A or B or C)	At least one of A, B and C occur
(A & B & C)	All three A, B and C occur
(A & not B & not C) or (B & not A & not C) or (C & not B & not A)	Exactly one of A, B and C occur
(A & not B & not C) or (B & not A & not C) or (C & not B & not A)	Exactly two of A, B and C occur
(A & not B & not C) or (B & not A & not C) or (C & not B & not A)	At most one of A, B and C occurs