Reading Quiz Section 6.1
1. Let A and B be sets. Let (a, b), (c, d) ∈ A × B. Then (a, b) = (c, d) if and only if
(a) a = c
(b) b = d
(c) ad = bc
(d) a = c and b = d
2. True or False: A × B = ∅ if and only if A = B = ∅.
3. Fill in the blank: If A and B are both finite nonempty sets, then max(|A|, |B|) |A × B|.
(a) =
(b) ≥
(c) ≤
(d) =
Practice Problems Section 6.1
1. Let A, B, C, D be sets. Prove
(A × B) ∩ ( C × D) = (A ∩ C) × (B ∩ D).
Video Solution
2. Let A and B be nonempty sets. Define a function π
1
: A × B → A by π
1
(a, b) = a. Show π
1
is
surjective. Under what conditions is it a bijection?
Video Solution
