Cos 203

Question 1

Mathematics can be classified into

Answer 1

Continuous and discrete maths

Question 2

Explain the classification of maths

Answer 2

a) continuous - it is based on the continuous number line and is characterized by the fact that between any two
Numbers there is almost always
an infinite set of
numbers
b) discrete - it involves distinct numbers I.e between any two points there is a countable number of points

Question 3

What is a set

Answer 3

A set is an unordered collection of different elements

Question 4

How can set be represented with example

Answer 4

a) rooster/ tabular method - elements of the set are listed, bounded by two braces and separated by commas.
b) set builder notation- the set is defined by specifying a property that each element of the set have in common.

Question 5

The meaning of each N Z Z^+ Q R W

Answer 5

N- natural number all positive integers
Z - integers all whole numbers in the number line
Z^+- all positive integers (N)
Q - rational numbers can be represented as a fraction
R - real numbers all rational and irrational numbers

Question 6

What is the cardinality of a set

Answer 6

The number of elements in a set

Question 7

What kind of function exists if the cardinality of X
a) = Y
b) is less than or equal to y
c) < y

Answer 7

a) Bijective function
b) injective function
c) there is an injective function but no bijective function

Question 8

Venn diagram was invented by who amdnin what year

Answer 8

John Venn 1800

Question 9

What is a venn diagram

Answer 9

Is a schematic diagram that shows all possible lovican relations between different mathematical set

Question 10

What is set union of a&b

Answer 10

A U B is a set of elements which are in a, b or both
A U B = {x|x £ A or x £ B}

Question 11

Set intersection of A and B

Answer 11

A n B is a set of elements which are in a and B
A n B ={x|x £ A and x £ B}

Question 12

Set difference or relative complement of A and B

Answer 12

A - B is a set of elements which are in only in a but not b
A - B = {x|x £ A and x is not an element of B}

Question 13

Cartesian product or cross product of set a and b

Answer 13

A X B is a set of ordered pair (a,b) where a E A and b E B

Question 14

What is the power set of set x

Answer 14

Its the set of all subset of x including its empty set.

Question 15

The cardinality of a power set is

Answer 15

2^n

Question 16

What is the partitioning of a set

Answer 16

Its the collection of n disjoint subset

Question 17

What conditions must the partitioning of a set satisfy

Answer 17

1) p1 must not contain an empty set
2) the union of all subset must be equal to the original set
3) the intersection of any two distinct subset must give an empty set

Question 18

What are the characteristics of a function

Answer 18

1) a function assigns to each element of a set exactly one element of a related set

2) a function of mapping f.x —> y, where d implies y is a relation from element of a set x to the elements of another set y. X is the domain and y is the co domain

3) the function f is the relation of x and y such that for each x E X exists a y E Y such that x,y are elements of the relation . In this x Is called the pre-image while y is called the image of function f

Question 19

List the types of functions we have

Answer 19

1) objective or one to one function
2) surjective function

Question 20

Explain objective or one to one function

Answer 20

The function A —> B is said to be inject if for ach b E B exists at most one a E A such that f(x) = T

{I.e. a1 is not equal to a2 and f(a1) is not equal to f(a2) and each element is a domain wraps up to a unique element in the co domain