Set theory

Question 1

Equivalent sets?

Answer 1

Two sets are equivalent when they have the same number of elements.

Question 2

Equal sets

Answer 2

They have the exact same elements

Question 3

Empty set

Answer 3

{}

Question 4

Subset

Answer 4

If every element of set A is in set B then set A is a subset of B.

(empty set is a subset of every set)
(a set is a subset of itself)

Question 5

Power set

Answer 5

2^n
(n is the number of elements in a set)

Question 6

List subsets of A = {1,3,5}

Answer 6

{}, {1}, {3}, {5}, {1,3}, {1,5}, {3,5}, {1,3,5}

Question 7

Cardinality of a set

Answer 7

Number of numbers in a set
n(A) = x
A = {1,2,3,4}
n(A) = 4

Question 8

Disjoint set

Answer 8

This means they have no elements in common

Question 9

Complement of a set

Answer 9

Complement of set A is a set of all the elements that are not in set A.
It is denoted by A’

Question 10

Difference of two sets

Answer 10

All the elements that are in set A but not in set B.
It is denoted by A\B or A-B

Question 11

Symmetric difference

Answer 11

All of elements of a set except their intercept.
C={1,2,3,4} D={2,4,6,7}
A△B= {1,3,6,7}

Question 12

Cartesian product of sets

Answer 12

Set of all possible ordered pairs
A={1,2} B={3,4}
AxB={ (1,3), (1,4), (2,3), (2,4)}