Question

4. If X = { 1, 2, 3, 4, 5 }, Y = { 1, 3, 5, 7, 9 } determine which of the following relations
from X to Y are functions? Give reason for your answer. If it is a function, state its
type.
(i) R1
= { ^ h x y, | y x = + 2, x X ! , y Y ! }
(ii) R2 = { (1, 1), (2, 1), (3, 3), (4, 3), (5, 5) }
(iii) R3 = { (1, 1), (1, 3), (3, 5), (3, 7), (5, 7) }
(iv) R4 = { (1, 3), (2, 5), (4, 7), (5, 9), (3, 1) }

Answer 1

QUESTION:
If X = { 1, 2, 3, 4, 5 }, Y = { 1, 3, 5, 7, 9 } determine which of the following relations
from X to Y are functions? Give reason for your answer. If it is a function, state its type.
(i) R1= {x y) | y =x + 2, x ∈X , y ∈Y !}
(ii) R2 = { (1, 1), (2, 1), (3, 3), (4, 3), (5, 5) }
(iii) R3 = { (1, 1), (1, 3), (3, 5), (3, 7), (5, 7) }
(iv) R4 = { (1, 3), (2, 5), (4, 7), (5, 9), (3, 1) }

•One - one function : f is called and one - one function if it takes different elements of A into the elements of B.
Co domain ≠ Range

•Onto function : A function is said to be an onto function if every element in B has preimage in A.
Co domain = Range

•Bijective function : This functions include both one - one and onto function.

•Domain : The set of all the first element of the ordered pairs of a relation is called the domain of the relation.

•Range : The set of all the second elements of the ordered pairs of a relation is called the range of the relation.

SOLUTION IS IN THE ATTACHMENT..

HOPE THIS WILL HELP YOU...

Answer 2

It is given that ,

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

B = { 1 , 3 , 5 ,7 , 9 }

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Function :

In a relation of no two ordered

pairs having same first

co-ordinates , then such relation

is called a function .

• Every element in A should have

an image .

***************************************

Here ,

1 ) R1 = { (x,y)/y=x+2,x€A, y€B }

R1 = {(1,3),(3,5),(5,7)}

R1 is not a function .

[ 2 , 4 has no image in B ]

2 ) R2 = { (1,1),(2,1),(3,3),(4,3),(5,5)}

R2 is a function.

[ No two ordered pairs have same

first coordinates ]

3 ) R3 = { (1,1),(1,3),(3,5),(3,7),(5,7)}

R3 is not a function.

[ First coordinates are same in

( 1 , 1 ) ,( 1 , 3 ) ]

4 ) R4 = {(1,3),( 2,5),(4,7),(5,9),(3,1)}

R4 is a function .

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