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Preliminaries · 1.1
Physics
Problem
Prove parts (2), (4), (5), and (6) of Proposition 1.2.2. That is, let
A
A
A
,
B
B
B
, and
C
C
C
be sets and show that: ((2))
A
∪
∅
=
A
A \cup \emptyset = A
A
∪
∅
=
A
and
A
∩
∅
=
∅
A \cap \emptyset = \emptyset
A
∩
∅
=
∅
; ((4))
A
∪
B
=
B
∪
A
A \cup B = B \cup A
A
∪
B
=
B
∪
A
and
A
∩
B
=
B
∩
A
A \cap B = B \cap A
A
∩
B
=
B
∩
A
; ((5))
A
∪
(
B
∩
C
)
=
(
A
∪
B
)
∩
(
A
∪
C
)
A \cup (B \cap C) = (A \cup B) \cap (A \cup C)
A
∪
(
B
∩
C
)
=
(
A
∪
B
)
∩
(
A
∪
C
)
; ((6))
A
∩
(
B
∪
C
)
=
(
A
∩
B
)
∪
(
A
∩
C
)
A \cap (B \cup C) = (A \cap B) \cup (A \cap C)
A
∩
(
B
∪
C
)
=
(
A
∩
B
)
∪
(
A
∩
C
)
.
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