Union intersection and complement of sets - One Line Questions
1.
The symmetric difference of two sets A and B, denoted by A Δ B, is defined as: —
(A ∪ B) - (A ∩ B)
2.
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is the union of A and B (A ∪ B)? —
{1, 2, 3, 4, 5, 6}
3.
If A = {1, 3, 5} and B = {2, 4, 6}, what is A ∪ B? —
{1, 2, 3, 4, 5, 6}
4.
If A = {x | x is a natural number less than 5} and B = {x | x is a natural number greater than 3 and less than 7}, what is A ∪ B? —
{1, 2, 3, 4, 5, 6}
5.
If A = {1, 2, 3} and B = {1, 2, 3}, what is A ∪ B? —
{1, 2, 3}
6.
If A = {1, 2, 3} and B = {1, 2, 3}, what is A ∩ B? —
{1, 2, 3}
7.
Let A = {1, 2, 3} and B = {3, 4, 5}. What is the set difference A - B? —
{1, 2}
8.
Let A = {1, 2, 3} and B = {3, 4, 5}. What is the set difference B - A? —
{4, 5}
9.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set and A = {2, 4, 6, 8}. What is the complement of A (A')? —
{1, 3, 5, 7, 9}
10.
If A = {prime numbers less than 10} and B = {odd numbers less than 10}, what is A ∩ B? —
{3, 5, 7}
11.
Using the sets from the previous question, what is A ∪ B? —
{1, 2, 3, 5, 7, 9}
12.
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is A Δ B? —
{1, 2, 5, 6}
13.
Using the sets from the previous question, what is A ∩ B? —
{4}
14.
Given A = {a, b, c} and B = {c, d, e}, what is the intersection of A and B (A ∩ B)? —
{c}
15.
If A = {apple, banana, cherry} and B = {banana, date, fig}, what is A ∩ B? —
{banana}
16.
Let U = {a, b, c, d, e} and A = {a, c}. What is A' ∩ A? —
∅
17.
If A = {vowels in the English alphabet} and B = {letters in the word 'EDUCATION'}, what is A ∩ B? —
{E, U, A, I, O}
18.
Using the sets from the previous question, what is A ∪ B? —
{E, D, U, C, A, T, I, O, N}
19.
Let U = {all integers} and A = {even integers}. What is A'? —
{odd integers}
20.
The complement of the complement of a set A is: —
A
21.
The formula for the number of elements in the union of two sets is given by: —
|A ∪ B| = |A| + |B| - |A ∩ B|
22.
If |A ∪ B| = 10, |A| = 6, and |B| = 7, what is |A ∩ B|? —
1
23.
If |A| = 5, |B| = 7, and |A ∩ B| = 3, what is |A ∪ B|? —
8
24.
Let U = {1, 2, 3, 4, 5} and A = {1, 2}. What is the number of elements in A'? —
3
25.
Let U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}. What is the number of elements in A ∪ A'? —
6
26.
If A ⊆ B, then A ∪ B is equal to: —
B
27.
For any set A, A ∪ A' is equal to: —
U (universal set)
28.
For any set A, A ∩ A' is equal to: —
∅ (empty set)
29.
If U is the universal set and A is any set, then A ∪ U is: —
U
30.
If U is the universal set and A is any set, then A ∩ U is: —
A
31.
If A ⊆ B, then A ∩ B is equal to: —
A
32.
What is the relationship between A - B and B - A? —
(A - B) ∪ (B - A) = A Δ B
33.
The distributive property of intersection over union states that: —
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
34.
The distributive property of union over intersection states that: —
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
35.
Which of the following is NOT a property of set intersection? —
A ∩ B = A ∪ B
36.
The elements that are in A and also in B are represented by: —
A ∩ B
37.
The elements that are in A or in B or in both are represented by: —
A ∪ B
38.
Which of the following is NOT a property of set union? —
A ∪ B = A ∩ B
39.
If A and B are any two sets, which of the following is always true? —
A ∩ B ⊆ A ∪ B
40.
If A ∩ B = A, this implies: —
A ⊆ B
41.
If A ∪ B = B, this implies: —
A ⊆ B
42.
What is (A ∪ B)'? —
A' ∩ B'
43.
What is (A ∩ B)'? —
A' ∪ B'
44.
Which property states that for any two sets A and B, A ∪ B = B ∪ A? —
Commutative Property of Union
45.
If A and B are two sets such that A ∩ B = A, then which of the following is true? —
A ⊆ B
46.
Which property relates union and intersection in the form A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)? —
Distributive Property
47.
Which property relates intersection and union in the form A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)? —
Distributive Property
48.
Which law states that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)? —
Distributive Law
49.
Which law states that (A ∩ B)' = A' ∪ B'? —
De Morgan's Law
50.
Which law states that (A ∪ B)' = A' ∩ B'? —
De Morgan's Law