Discrete Math Quiz
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SETS, RELATIONS, AND FUNCTIONS
Question 1
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Which of the following set identities is equivalent to the distributive law
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
)
?
A
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
)
by duality principles
B
(
A
∪
B
)
c
=
A
c
∩
B
c
(A \cup B)^c = A^c \cap B^c
(
A
∪
B
)
c
=
A
c
∩
B
c
by De Morgan's laws applied twice
C
A
∖
(
B
∩
C
)
=
(
A
∖
B
)
∪
(
A
∖
C
)
A \setminus (B \cap C) = (A \setminus B) \cup (A \setminus C)
A
∖
(
B
∩
C
)
=
(
A
∖
B
)
∪
(
A
∖
C
)
by complement distribution
D
A
△
(
B
∪
C
)
=
(
A
△
B
)
△
C
A \triangle (B \cup C) = (A \triangle B) \triangle C
A
△
(
B
∪
C
)
=
(
A
△
B
)
△
C
by symmetric difference associativity
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