यदि X = {1, 2, 3, 4, 5} और Y = {1, 3, 5, 7, 9} तो ज्ञात कीजिए कि निम्नलिखित समुच्चयों में कौन-कौन X से Y पर फलन हैं?
(i) `R_(1)` = {(x, y) : y = x + 2, x `in X, y in Y}`
(ii) `R_(2)` = {(1, 1), (2, 1), (3, 3), (4, 3), (5,5)}
(iii) `R_(3)` = {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)}
(iv) `R_(4)` = {(1, 3), (2, 5), (4, 7), (5, 9), (3, 1)}

Let X = {1, 2, 3, 4} and Y = {1, 3, 5, 7,9} . Which of the following is relations from X to Y (i) R_(1) = {(x, y):y=2+x,x inX, yinY} (ii) R_(2) = {(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)} (iii) R_(3) = {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)} (iv) R_(4) = {(1, 3), (2, 5), (2, 4), (7, 9)}

If X = {1,2,3,4,5}, Y = {1,3,5,7,9} determins which of the following relations from X to Y are functions ? Give reasonfor your answer. If it is a function. State its type. (i) R_(1) = {(x,y) | y = x + 2, x in X , y in Y } (ii) R_(2) = {(1,1),(2,1),(3,3),(4,3),(5,5)} (iii) R_(3) { (1,1),(1,3),(3,5),(3,7),(5,7)} (iv) R_(4) {(1,3),(2,5),(4,7),(5,9),(3,1)}

Let X = {1,2,3,4,5} and Y = { 1,3,5,7,9}. If R_(2) ={ (1,1), (1,3), (3,5), (3,7), (5,7) } then R_(2) is a relation from X to Y because

1 + 5x + 3y = 9 2x 3y = 12 X = (x, y) - 4

Find R^(-1) , when (i) R={(1,2),(1,3),(2,3),(3,2),(4,5)}, (ii) R={(x,y):x,yinN,x+2y=8}.

Find x and y if: (i) (x + 1,y-2) = (3,1) (ii) (x + 2,4)= (5,2x+y)

A= {1, 2, 3, 4, 5} R = {(x,y) ||x^(2)-y^(2) | lt 16} Find R.