Question

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

• A. {(0,10),(1,7),(2,4),(3,1)}
• B. {(0,10),(1,7),(2,4),(3,0)}
• C. {(0,10),(1,6),(2,3),(3,1)}
• D. {(0,10),(1,7),(4,2),(1,3)}

Answer 1

The correct option is A {(0,10),(1,7),(2,4),(3,1)}

3x + y = 10 $\Rightarrow$ y = 10 - 3x
Given, x and y are whole numbers.
$\therefore$ When x = 0 , y = 10 - 3$\times$0 = 10
When x = 1 , y = 10 - 3$\times$1 = 7
When x = 2 , y = 10 - 3$\times$2 = 4
When x = 3 , y = 10 - 3$\times$3 = 1
When x = 4 , y = 10 - 3$\times$4 = -2 which is not a whole number.
Now, if we try for more values of x $\in$ W , we find that in each case, the value of y obtained does not belong to set W.
$\therefore$ The ordered pairs, which satisfy the given relation are (0,10),(1,7),(2,4) and (3,1) only.
The required relation = {(0,10),(1,7),(2,4),(3,1)}