# Question: let a 1 2 3 and b 2...

###### Question details

Let A = {1, 2, 3} and B = {2, 3, 4, 5}. Find the cardinalities
of the

following sets:

(i) A ∪ B

(ii) A ∩ B

(iii) A \ B

(iv) B \ A

(v) P(A ∪ B)

Exercise 1.2. Let A = {◦, {◦}, {∅}} and let B = {∅, {◦}}. Find
the cardinalities of

the following sets:

(i) A ∪ B

(ii) A ∩ B

(iii) A \ B

(iv) A × B

(v) P(A)

Exercise 1.3. Find the cardinality of the set

\

n∈N

[0, 1/n].

Exercise 1.4. Prove distributive property (1.3.6), that for any
sets A, B, and C, we

have that

(A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C).