Question

Let A = {2,3) and B = {2,3,4}. If a relation from A to B is defined by R = {(x, y) :x + y = 5), find R.

a) R = {(x, y) : x + y = 5}
b) R = {(x, y) = x + y = 6)
c)R= {(x, y) : y = x^2}
d) R = {(x, y) : x=y}
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Answer 1

Explanation:

Finding cartesian product :

A×B

= {2,3} × {2,3,4}

= {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}

so

R = {(x,y):x+y=5}

so, R1 ={(2,3),(3,2)}

b) - R2 = {(2,4),(3,3)}

c) - R3 = {(2,4)}

d) - R4 = {(2,2),(3,3)}