Q. 6

If R = {(x, y): x

Answer :

Range means the set of permissible values of y

Now x and y should lie in a set of natural numbers because the relation is on N


x + 2y = 8


2y = 8 – x


y = 1/2(8 – x) …(i)


Now if we put x > 8 y will be negative which is not in set N (that is not a natural number)


For y to be a natural number (8 – x) has to be an even number


As 8 – x is even, and x has to be less than or equal to 8 hence x can be 8, 6, 4, 2 and 0


Now when we put these values of x in (i), we will get corresponding y values


Hence y = 0, 1, 2, 3 and 4 respectively


Hence range is {0, 1, 2, 3, 4}.


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