Reading Quiz Section 4.2
1. Let U = Z, A = 2Z, B = {1, 3, 5}. Which of the following statements are true?
(a) B ⊆ A
C
.
(b) A and B are not disjoint
(c) A ∪ B = Z.
(d) Z \ B is finite
(e) A
C
= 2Z + 1
2. True or False: if A and B are sets, then B ⊆ A ∪ B.
3. For sets A and B, the result that (A ∪ B)
C
= A
C
∩ B
C
is most similar to which of the following
laws of logic?
(a) Law of double negation
(b) Law of absorption
(c) De Morgan’s law(s)
(d) Law of associativity
4. For sets A and B, which of the following are true?
(a) A ∩ B ⊆ A \ B
(b) B = (A ∩ B) ∪ (B \ A)
(c) A ∪ B = (A \ B) ∪ (A ∩ B) ∪ (B \ A)
(d) A \ B = B \ A
Practice Problems Section 4.2
1. Let a, b, c, d ∈ R. Show
(a, b) ∩ (c, d) =
max{a, c}, min{b, d}
where we take the convention that (α, β) = ∅ if β < α.
Video Solution
2. Let U be a universal set and A and B sets. Prove that (A \ B)
C
= A
C
∪ B.
Video Solution
3. Let A be a set. Prove that if A ∪ B ⊆ B for every set B, then A = ∅.
Video Solution
