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**Ques 1: Find a and b if (a – 1, b + 5) = (2, 3)If A = {1,3,5}, B = {2,3} find : (Question-2, 3) (i) A × B (ii) Let A = {1,2}, B = {2,3,4}, C = {4,5}(iii) A × (B ∩ C)**

(i) A × B = {(1,2), (1,3), (3,2), (3,3), (5,2), (5,3)}

(ii) B × A = { (2,1), (2,3), (2,5), (3,1), (3,3), (3,5)}

(ii) {(1,4), (2,4)}

(iv) {(1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), (2,5)}

Ans:

(i) Not a function because 4 has two images.

(ii) Not a function because 2 does not have a unique image.

∴ n(A * B)= ∩(A) * ∩(B)= mk

∴ the number of subsets of A x B = 2mk

∵ n(A) =m, then the number of subsets of A = m

Since every subset of A * B is a relation from A to B therefore the number of relations from A to B = 2

Ques 5: Let f = {(1,1),(2,3),(0,-1),(-1,3),........} be a function from z to z defined f(x) ax +b, by for same integers a and b determine a and b.

Since (1,1) ∈ f

(2,3) ∈ f.f (2) = 3 ⇒ 2a+b =3........(ii)

Subtracting (i) from(ii) we set a=2

Substituting a = 2 is (ii) we get 2+b=1

⇒ b = -1

Hence a = 2, b = -1

Ques 6: Express {(x,y): y+ 2x =5, xy ∈ w} as the set of ordered pairs

Ans:

Put x=0, y+0= 5 ⇒ y=5

x=1, y+2*1= 5⇒ y =3

x=2,y+2*2=5 ⇒ y=1

For anther values of x∈w , we do not get y∈w

Hence the required set of ordered peutes is {(0'5),(1,3),(2,1)}

Ans:

Ans:

A to B therefore R = [ (-1,0),(2,3),(5,6) ]

Domain of R = {-1,2,5} and range of R = {0,3,6}

.

Is the following true implies a,b ∈ R implies (b,a) ∈ R

Ans:

Ques 12: Let be the set of natural numbers and the relation R be define in N by R = what is the domain, co domain and range of ? Is this relation a function?

∴ Domain of R = N. co domain of R = N and Range of R is the set of even natural numbers.

Since every natural number x has a unique image 2x therefore, the relation R is a function.

Ans:

is f a function justify your answer

Ans:

∴ One element 1/2 have two images

∴ f is not function

Ans:

f (o) = 32

Ans:

= 0**Ques 17: If A and B are two sets containing m and n elements respectively how many different relations can be defined from A to B ?Ans: **2

(a) Depict this relation using arrow diagram.

(b) Find domain of R.

(c) Find range of R.

(d) Write co-domain of R.

(b) {1,2,3,4}

(c) {1,4,9,16}

(d) {1,4,9,16,25}

(ii) Codomain

(iii) Range Is this relation a function from N to N

(ii) N

(iii) Set of even natural numbers yes, R is a function from N to N.

Ans:

Range is [–3, ∞)

Ans:

Range = {2}

Then

(i) Find the domain and the range of R

(ii) Write R as a set of ordered pairs.

Ans:

Put

for all the values x y ϵ

∴ domain of R = {0,1,2,3,4} and range of R = {8,6,4,2,0}

(ii) R as a set of ordered pairs can be written as

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