sets hard

Sets Quiz (Hard)

1. In set theory, what is the Cartesian product of two sets A and B?

a) The set of all elements of set A b) The set of all ordered pairs (a, b) with a ∈ A and b ∈ B c) The set of all subsets of set A

2. If A = {1, 2, 3} and B = {3, 4, 5}, what is A × B?

a) {(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5)} b) {(1, 1), (2, 2), (3, 3), (1, 3), (2, 3), (1, 4), (2, 4), (3, 5)} c) {(1, 1), (2, 2), (3, 3), (1, 4), (2, 5), (3, 3)}

3. What is the number of subsets of a set with n elements?

a) n b) 2^n c) n!

4. What is the number of proper subsets of a set with n elements?

a) n b) 2^n c) 2^n - 1

5. What is the value of n if A = {1, 2, 3, ..., n} and B = {2, 4, 6, ..., 2n}?

a) n = 2 b) n = 3 c) n = 4

6. In set theory, what does the distributive property A ∪ (B ∩ C) equal to?

a) A ∪ B ∩ C b) (A ∪ B) ∩ C c) A ∪ (B ∪ C)

7. In set theory, what does the distributive property A ∩ (B ∪ C) equal to?

a) A ∪ B ∩ C b) (A ∪ B) ∩ C c) A ∪ (B ∪ C)

8. In set theory, the complement of the empty set is:

a) The empty set b) A universal set c) It is undefined

9. In set theory, if A is a subset of B, then A ∩ B is equal to:

a) A b) B c) The empty set

10. In set theory, the union of two disjoint sets is equal to:

a) A b) B c) The empty set