Algebraic properties of sets - One Line Questions
1.
What is the result of A ∩ (B ∪ C) according to the distributive property? —
(A ∩ B) ∪ (A ∩ C)
2.
What is the result of A ∪ ∅, where ∅ is the empty set? —
A
3.
If U is the universal set, then A ∪ U is equal to: —
U
4.
The intersection of any set A with the empty set ∅ is: —
∅
5.
If A ⊆ B, what is A ∪ B equal to? —
B
6.
If A ⊆ B, what is A ∩ B equal to? —
A
7.
What is the idempotent property for intersection of a set with itself? —
A ∩ A = A
8.
The property A ∩ (A ∪ B) = A is known as: —
Absorption Property
9.
Which property implies that A ∪ B = B ∪ A? —
Commutative
10.
Which property implies that A ∩ B = B ∩ A? —
Commutative
11.
Which property states that A ∪ B = B ∪ A and A ∩ B = B ∩ A? —
Commutative Property
12.
Which property ensures that the order of sets does not matter in union or intersection? —
Commutative Property
13.
Which property demonstrates that A ∩ B = B ∩ A for any sets A and B? —
Commutative Property of Intersection
14.
The property that states A ∪ B = B ∪ A for any sets A and B is called: —
Commutative Property of Union
15.
Which property ensures that if we take the union of a set with itself, the result is the same set? —
Idempotent
16.
Which property is related to the identity element for union being the empty set? —
Identity
17.
Which property is related to the identity element for intersection being the universal set? —
Identity
18.
Which property states that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)? —
Distributive
19.
Which property is demonstrated by A ∪ ∅ = A? —
Identity
20.
If A ⊆ B, then A ∪ B = B and A ∩ B = A. These are consequences related to: —
Properties of subsets
21.
The property A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) is an application of the: —
Distributive Law
22.
The property A ∪ A = A is an example of: —
Idempotent Property
23.
Which property states that A ∪ (A ∩ B) = A? —
Absorption Property
24.
The property A ∩ A = A is an example of: —
Idempotent Property
25.
Which property is demonstrated by A ∪ ∅ = A? —
Identity Property
26.
Which property can be stated in two forms: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) and A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)? —
Distributive Property
27.
The property A ∩ (A ∪ B) = A is also known as: —
Absorption Property
28.
The property (A ∪ B) ∪ C = A ∪ (B ∪ C) is an example of: —
Associative Property
29.
The property (A ∩ B) ∩ C = A ∩ (B ∩ C) is an example of: —
Associative Property
30.
Which property is demonstrated by A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)? —
Distributive Property
31.
The property A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) is an example of: —
Distributive Property
32.
Which property states that A ∪ ∅ = A and A ∩ U = A? —
Identity Property
33.
The property A ∪ A = A and A ∩ A = A are examples of: —
Idempotent Property
34.
The property A ∩ U = A, where U is the universal set, demonstrates the: —
Identity Property
35.
The property (A ∩ B) ∩ C = A ∩ (B ∩ C) is called: —
Associative Property of Intersection
36.
Which property states that for any sets A, B, and C, the union of A with the union of B and C is the same as the union of the union of A and B with C? —
Associative Property of Union
37.
The property (A ∪ B) ∪ C = A ∪ (B ∪ C) is called: —
Associative Property of Union
38.
Which property relates union and intersection in the form A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)? —
Distributive Property of Union over Intersection
39.
The property that states A ∪ A = A is the property of: —
Idempotence
40.
The property A ∩ A = A is the property of: —
Idempotence
41.
The property A ∩ (A ∪ B) = A is also known as the: —
Absorption Law
42.
The property A ∪ (A ∩ B) = A is known as: —
Absorption Property
43.
Which property states that for any sets A and B, A ∪ (A ∩ B) = A? —
Absorption Property
44.
The property A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) is known as: —
Distributive Property of Intersection over Union
45.
The property A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) is known as: —
Distributive Property of Union over Intersection
46.
The property A ∩ ∅ = ∅ is an example of: —
Identity Property
47.
Which property states that A ∪ U = U, where U is the universal set? —
Identity Property
48.
The property A ∩ U = A, where U is the universal set, is an example of: —
Identity Property
49.
The property A ∪ (B ∪ C) = (A ∪ B) ∪ C applies to which operation? —
Union only
50.
For any set A and the universal set U, A ∩ U is equal to: —
A