Sets and Notation

Question 1

What is a set?

Answer 1

A set is a collection of objects which are known as elements or members.

Question 2

What is the cardinality or order of a set and how is it written?

Answer 2

It tells you the number of elements in a set (non-recurring) and |A|

Question 3

How do you draw on a number line, [0,5)?

Answer 3

Filled circle on 0, line to empty circle on 5

Question 4

Difference between closed and open brackets with sets?

Answer 4

Closed brackets [,] include the limits, open brackets exclude the limits

Question 5

What does A⊂B mean?

Answer 5

That every element in A is in B but A =/= B

Question 6

When does the set A = set B?

Answer 6

When A⊂=B and B⊂=A

Question 7

When is AnB the case?

Answer 7

{x:(x∈A) and (x∈B)}

Question 8

When is AUB the case?

Answer 8

{x:(x∈A) or (x∈B)}

Question 9

When is A\B the case?

Answer 9

{x:(x∈A) and (x!∈B)}

Question 10

What are 2 ways to write the empty set?

Answer 10

{},∅

Question 11

An(BnC) =?

Answer 11

(AnB)nC

Question 12

AU(BUC)=?

Answer 12

(AUB)UC

Question 13

3 properties of addition?

Answer 13

Commutativity, associativity and distributive

a+b = b+a, a+(b+c) = (a+b) + c, a(b+c) = ab + ac

Question 14

How do you show that something is true or false?

Answer 14

Proof or counterexample (respectively)

Question 15

The complement of A, A’ =

Answer 15

{x∈U: x∈A}

Question 16

State de Morgan’s Laws

Answer 16

(AUB)' = A'nB'
(AnB)' = A'UB'

Question 17

Show the distributivity laws for An(BUC) and Au(BnC)

Answer 17

An(BUC) = (AnB)U(AnC)
Au(BnC) = (AuB)n(AuC)