1. Math
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  3. let a 1 2 3 and b 2...

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).

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