Representation of Relations

Q. The given Arrow Diagram represents a relation between A and B. How do we represent this relation in Set-Builder form?

1. R = {(x, y) $\in$ A$\times$B : y +1 is two more than x}
2. R = {(x, y) $\in$ A$\times$B : y is one more than twice of x}
3. R = {(x, y) $\in$ A$\times$B : y is one less than twice of x}
4. R = {(x, y) $\in$ A$\times$B : x is one more than twice of y}

Q.

Five years ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? [3 MARKS]

Q. Express the relation {(x, y) : 3x + y = 10 ; x, y $\in$ W} as the set of ordered pairs.

1. {(0, 10), (1, 7), (2, 4), (3, 1)}
2. {(0, 10), (1, 7), (4, 2), (1, 3)}
3. {(0, 10), (1, 6), (2, 3), (3, 1)}
4. {(0, 10), (1, 7), (2, 4), (3, 0)}