Let `X = {1, 2, 3, 4}` and `Y = {1, 3, 5, 7,9}`. Which of the following is relations from X to Y

Options

A. `R_(1) = {(x, y):y=2+x,x inX, yinY}`
B. `R_(2) = {(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)}`
C. `R_(3) = {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)}`
D. `R_(4) = {(1, 3), (2, 5), (2, 4), (7, 9)}`

Answer

A, B, C

Explanation

X = {1, 2, 3, 4, 5}
Y = {1, 3, 5, 7, 9}
(a) `R_(1) = {(x, y):y=2+x,x inX, y inY}`
`{:(x=1,y=2),(x=2,y=4),(x=3,y=5),(x=4,y=6),(x=5,y=7):}`
So, `R_(1)` is a relation from X to Y.
(b) `R_(2) = {(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)}`
`R_(2) sube X xx Y`
(c ) `R_(3)` = {(1, 1), (1, 3), (3, 5), (5, 7)}
`R_(3)subeXxxY`
(d) `R_(4)cancelsubeXxxY`