Abstract Algebra: Theory and Applications · Problem 1.1

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · set-theory-operations

Problem

Prove parts (2), (4), (5), and (6) of Proposition 1.2.2. That is, let

A

B

, and

C

be sets and show that: ((2))

A \cup \emptyset = A

and

A \cap \emptyset = \emptyset

; ((4))

A \cup B = B \cup A

and

A \cap B = B \cap A

; ((5))

A \cup (B \cap C) = (A \cup B) \cap (A \cup C)

; ((6))

A \cap (B \cup C) = (A \cap B) \cup (A \cap C)