Sets 1

Question 1

Set

Answer 1

Unordered collection of elements.

Question 2

Element (2)

Answer 2

1) a ∈ A -> a is an element of set A

2) a ∉ A -> a is not an element of set A

Question 3

Subset (2)

Answer 3

1) A ⊆ B -> every element of A is in set B

2) A ⊄ B -> at least one element of A is not in B

Question 4

Set Equality

Answer 4

A = B if A ⊆ B and B ⊆ A

Question 5

Union (2)

Answer 5

1) A ∪ B := {x ∈ U : x ∈ A : x ∈ B }

2) All elements in A or B

Question 6

Intersection (2)

Answer 6

1) A ∩ B := {x ∈ U : x ∈ A and x ∈ B}

2) Elements which are both in A and B

Question 7

Minus (2)

Answer 7

1) A \ B := {x ∈ U : x ∈ A and x ∉ B} (or A ∩ B’)

2) Elements which are in A but not in B

Question 8

Symmetric difference (2)

Answer 8

1) A △ B := (A ∪ B) ∩ (A ∩ B)’

2) Elements either in A or B

Question 9

Algebra Definitions (2)

Answer 9

1) A \ B = A ∩ B’

2) A △ B = (A ∪ B) ∩ (A ∩ B)’

Question 10

Algebra De Morgan’s (2)

Answer 10

1) (A ∩ B)’ = A’ ∪ B’

2) (A ∪ B)’ = A’ ∩ B’

Question 11

Algebra Distributivity (2)

Answer 11

1) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

2) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)