Question

Consider the following with regard to a relation R on a set of real numbers defined by xRy if and only if 3x+4y=5
I. 0 R 1 II. `1 R(1)/(2)`
III. `(2)/(3)R(3)/(4)`
Which of the above are correct?
A. I and II
B. I and III
C. II and III only
D. I, II and III

Answer 1

Correct Answer - C
Let on the set of real numbers, R is a relation defined by xRy if and only if 3x+4y=5
(I) Put x=0 and y=1, we get
LHS=3(0)+4(1)=`4ne5` (=RHS)
Hence 0 is not related to 1.
(II) Now, Put x=1 and `y=(1)/(2)`, we get
`LHS=3(1)+4xx(1)/(2)=5=5(=RHS)`
Hence 1 is related to `(1)/(2)`.
(III) Similarly, `(2)/(3)` is related to `(3)/(4)`.
Hence, both statements II and III are correct.