Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y) : y=2x, y in N} ,

Write the following relation in roster from R = {(x,y): x-2y, x in A, y in B} where A= {2, 3, 4, 5, 6} B= {1, 2,3}

Number of ordered pair (x,y) which satisfies the relation (x^(4)+1)/(8x^(2))=sin^(2)y*cos^(2) y , where y in [0,2pi]

U= {1, 2, 3, 4} and relation R = {(x,y): y gt x, x, y in U} then range of R is …….

Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9). Let R_1 be a relation in X given by R_1 = {(x, y) : x - y is divisible by 3} and R, be another relation on X given by R_2 = {(x, y) : {x, y}sub {1, 4, 7}} or {x,y} sub{2,5,8} or {x,y} sub {3,6,9} . Show that R_1 = R_2 .

A = {(1,2,3,......10} The relation R defined in the set A as R = {(x,y) : y = 2x} . Show that R is not an equivalence relation.

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R is the set N of natural numbers defined as R = {(x,y): y = x +5 and x lt 4 } .

Determine w hether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1,2,3,…,13,14} defined as R = {(x,y): 3x -y =0} (ii) Relation R in the set N of natural numbers defined as R = {(x,y): y = x +5 and x lt 4} (iii) Relation R in the set A ={1,2,3,4,5,6}as R = {(x,y):y is divisible by x} (iv) Relation R in the set Z of allintegers defined as R= {(x, y) : x -y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x,y) : x and y work at the same place} (b) R = {(x,y):x and y live in the same locality] (c ) R ={(x,y) :x is exactly 7 cm taller than y} (d) R = {(x,y) :x is wife of y} (e) R = {(x,y):x is father of y}

Find the area bounded by the lines y= 4x + 5 , y=5 -x and 4y = x +5.