Michael Sipser Edition 3 Exercise 0 Question 3 (Page No. 26)

Question

Let A be the set {x, y, z} and B be the set {x, y}.

a. Is A a subset of B?

b. Is B a subset of A?

c. What is A ∪ B?

d. What is A ∩ B?

e. What is A × B?

f. What is the power set of B?

Answer 1

a) Yes ,but not all cases

b) Yes

c) AUB = {x,y,z}

d) A ∩ B = {x,y}

e) A X B = {x,y,z} X {x,y}

               = {(x,x),(x,y),(y,x),(y,y),(z,x),(z,y)}

f) P(B)= { Φ,{x},{y},{x,y}}