Sets and Relations

Question 1

Set definition

Answer 1

well defined collection of objects

Question 2

What is roster form of sets and what is it also known as

Answer 2

Braces form
{1,2,3,4,5,6,7,8,9}

Question 3

Set Builder form also known as

Answer 3

Algebraic form or rule method or property method

Question 4

Can set contain infinite elements

Answer 4

Yes, sets can contain finite and infinite number of elements

Question 5

N

meaning of symbol

Answer 5

Natural numbers

Question 6

W

meaning symbol

Answer 6

Whole numbers

Question 7

Meaning of P⊂Q

Answer 7

P is subset of Q or all elements of P are contained in Q or Q is superset of P

Question 8

Proper subset

Answer 8

If all elements of P are in Q BUT P is not equal to Q then P is proper subset of Q

Question 9

What 2 special sets are included in subsets

Answer 9

The set itself and null/void set.

Question 10

Number of subsets

Answer 10

2^n

Question 11

Number of proper subsets

Answer 11

2^n-1

Question 12

disjoint sets

Answer 12

Where intersection between 2 sets is null set

Question 13

opposite of disjoint sets also called

Answer 13

overlapping/intersecting sets

Question 14

is {0} a null set

Answer 14

No, it is not null set as it has 0 as an element

Question 15

Singleton set

Answer 15

only one element

Question 16

Equal sets

Answer 16

A is subset of B and vice versa. Number of elements and elements are same

Question 17

repetition in sets

Answer 17

not required

Question 18

De Morgan’s law

Answer 18

(AUB)’ = A’∩B’ etc

Question 19

Cardinal number

Answer 19

total number of distinct elements in a set

Question 20

The important 2 set formula

Answer 20

n(AUB) = n(A) + n(B) - n(A∩B)

Question 21

The important 3 set formula

Answer 21

n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C) = n(AUBUC)

Question 22

Equivalent sets

Answer 22

number of elements same not elements themselves

Question 23

Power set

Answer 23

collection of all subsets of set

Question 24

ordered pair

Answer 24

two elements in a specified order are called ordered pair.

Question 25

Number of elements in product of 2 sets A and B

Answer 25

n(A)*n(B)

Question 26

Relation meaning

Answer 26

subset of product set

Question 27

function meaning

Answer 27

first element in ordered pairs is always different

Question 28

(a,b) what are a & b called

Answer 28

a- pre image b- image

Question 29

f:A->B what is A & B + what is range

Answer 29

A is domain B is co-domain range is the values we get by putting elements of A in the function that are included in B

Question 30

-What is one one function -also called as -condition

Answer 30

every different pre image has a different image injective function x1=x2 from f(x1)=f(x2)

Question 31

-Onto function -What it is also known as -Condition

Answer 31

If every element of the co-domain has a pre-image in domain. Range=Co-domain x= becomes y=

Question 32

Bijection function

Answer 32

Both onto and one-one

Question 33

Identity function | specify if its one one and onto

Answer 33

f(A->A) (x=y for all x belongs to A) {(1,1),(2,2)} It is both one-one and onto

Question 34

Constant function

Answer 34

All pre-images have only one image, range is a singleton set

Question 35

Equal function condition

Answer 35

same domain of f & g and satisfies f(x)=g(x)

Question 36

Composite function

Answer 36

fog or f(g) gof or g(f) if f(1)=3 and g(3)=9 then g(f(1))=9 or gof(1)=9

Question 37

Inverse function condition how to inverse

Answer 37

f has to be one-one onto function/bijection to be inverted. How to inverse - f(x)=x+1 - f(x)-1=x - x-1 is inverse function

Question 38

reflexive relation of {1,2,3,4} also called

Answer 38

{(1,1),(2,2),(3,3),(4,4)} even if one is missing then its not a reflexive relation. also called identity relation

Question 39

symmetric relation

Answer 39

(a,b),(b,a)

Question 40

transitive relation

Answer 40

(a,b) (b,c) then (a,c)

Question 41

equivalence relation

Answer 41

relation is reflexive, symmetric and transitive.

Question 42

in inverse what happens to domain and range

Answer 42

range becomes domain and domain becomes range

Question 43

{(1,1) (2,2)} from {1,2} is T,R,S,E

Answer 43

equivalence relation

Question 44

limit f(x) exists when

Answer 44

left hand limit and right hand limit exist and are equal

Question 45

1/x-a find limit

Answer 45

doesnt exist

Question 46

value of e

Answer 46

2.7183

Question 47

sum, difference, division (denominator isn't 0) and product of two continuous functions is

Answer 47

continuous function

Question 48

How to find point of discontinuity

Answer 48

where function is undefined