Sets

Question 1

What is specification?

Answer 1

Description of what the type does and the method it provides to do it.

Question 2

What is implementation?

Answer 2

Code that actually does the work

Question 3

What is a set?

Answer 3

A set is a group of things, either related or unrelated.

Question 4

Does a set have to contain a group of things which are related?

Answer 4

No, it the set can contain either related or unrelated elements.

Question 5

Does the order within a set matter?

Answer 5

No

Question 6

Do sets contain duplicates?

Answer 6

No

Question 7

What does ‘aEs’ mean?

Answer 7

‘a’ is a member of set ‘s’

Question 8

What does ‘4E{1,2,3,4}’ mean?

Answer 8

‘4’ is a member of set ‘{1,2,3,4}

Question 9

What would you change to ‘12E{1,2,3,4}’ to show that 12 is not part of the set.

Answer 9

Put a horizontal line through the E-like shape

Question 10

What does ∅ signify?

Answer 10

An empty set or a null set.

Question 11

What is U?

Answer 11

The universal set

Question 12

{1,2,3,4,5} = {3,2,4,1,5}

Is this correct?

Answer 12

Yes, they both equal each other despite the differing order.

Question 13

{1,2,3,4,5} = {1,2,3,3,4,2,1,5}

Is this correct?

Answer 13

Yes, because within sets duplicates are not important.

Question 14

{1,2,3,4} = {1,2,3,4,5}

Is this correct?

Answer 14

No, for they do not contain the same elements.

Question 15

S = {2,3,4,5}
T = {1,2,3,4,5,6}

Which, if any, is the subset?

Answer 15

S is the subset as all of its elements are contained with T.

Question 16

What does an underline ‘c’ symbol indicate?

For example, XcV?

Answer 16

It indicates that the first set is a subset of the second set.
X is a subset of V.

Question 17

How would you indicate that X is not a subset of V?

Answer 17

XcV with ‘c’ being underlined and a horizontal line going though it.

Question 18

S = {1,2,3}
T = {1,2,3,4}

Is S a subset or also a proper subset of T?

Answer 18

S is a proper subset of T because it does not equal itself.

Question 19

Can S be a subset of S?

Answer 19

Yes, all sets can subsets of themselves.

Question 20

What is the powerset of B = {1,2}?

Answer 20

P(B) = { {}, {1}, {2}, {1,2} }

Question 21

What is the powerset of C = {1,2,3}

Answer 21

P(C) = { {}, {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3} }

Question 22

What is the powerset of D = {Coleraine, Belfast}

Answer 22

P(D) = { {}, {Coleraine}, {Belfast}, {Coleraine, Belfast} }

Question 23

What does |A| mean?

Answer 23

The cardinality of A ie the number of elements in set A.

Question 24

What is the cardinality of A = {1,2,3,4,5}

Answer 24

|A| = 5

Question 25

What is the cardinality of S = { ∅, {A}, {B}, {A,B} }?

Answer 25

|S| = 4

Question 26

{1,2,3}U{3,4,5} = ?

Answer 26

{1,2,3,4,5}

Question 27

{1,2}U∅ = ?

Answer 27

{1,2}

Question 28

{1,2,3}n{3,4,5} = ?

Answer 28

{3}

Question 29

{1,2}n∅ = ?

Answer 29

∅

Question 30

What is a disjoint set?

Answer 30

Disjoint sets have no elements in common.

Question 31

{1,2,3} - {3,4,5} = ?

Answer 31

{1,2}

Question 32

What does (AUB)' mean?

Answer 32

' means complement. | This means that everything that not within the A and B union.

Question 33

What is the difference between a set and a multiset?

Answer 33

In a set, duplicates are not allowed. | In a multiset, duplicates are allowed.

Question 34

Is {1,2,3,4,4} a set or a multiset?

Answer 34

A multiset because it has duplicates.

Question 35

{a,a,a,b,b,c,c,d,d,d} | What is the multiplicity of a?

Answer 35

3

Question 36

{a,a,a,b,b,c,c,d,d,d} | What is the multiplicity of d?

Answer 36

3

Question 37

{a,a,a,b,b,c,c,d,d,d} | What is the cardinality of the above multiset?

Answer 37

10

Question 38

{1,3,6,1,3,1}U{1,7,6,1,3,6} = ?

Answer 38

{1,1,1,3,3,6,6,7} Only the max number of values from the multiset containing the most is taken.

Question 39

{1,3,6,1,3,1}n{1,7,6,1,3,6} = ?

Answer 39

{1,1,3,6} Only the min number of values is taken from each multiset where each multiset has the same value.

Question 40

In an array 0-4, values with a set are ? when | false, true, true, false, true

Answer 40

{1,2,4}

Question 41

How could you represent this multiset in an array 0-9? | {2,4,7,2,4,2,4,6,6}

Answer 41

{0,0,3,0,3,0,2,1,0,0}