Question

Let N be the set of all natural numbers, and let R be a relation on N defined as ∈and R=(x,y):x∈N and x+3y=15. Then

R as a set of ordered pairs is:

A) (3,4),(5,3),(9,2),(13,2)
B) (3,5),(2,7),(9,2),(12,1)
C) (3,4),(6,3),(9,2),(12,1)
D) (4,5),(7,3),(4,5),(4,2)

Answer 1

The relation R as a set of ordered pairs of natural numbers that satisfy the equation x + 3y = 15 is option C: (3, 4), (6, 3), (9, 2), (12, 1).

Step-by-step explanation:

The relation R on the set of all natural numbers N is given by R = (x, y) . To find R as a set of ordered pairs, we must find all pairs of natural numbers (x, y) that satisfy the equation x + 3y = 15. We solve this problem by using trial and error, plugging natural numbers into the equation and checking if they satisfy it.

Let's solve for possible values of x and y that satisfy the equation:

1. For y = 1, x + 3(1) = x + 3 = 15, so x = 15 - 3 = 12. Therefore, (12, 1) is a pair in the relation R.
2. For y = 2, x + 3(2) = x + 6 = 15, so x = 15 - 6 = 9. Therefore, (9, 2) is another pair in the relation R.
3. We continue this process for other values of y until we exhaust all natural numbers that give a natural number for x after solving the equation.

Hence, the correct answer with all the pairs of (x, y) that satisfy the equation x + 3y = 15, and where both x and y are natural numbers, is option C: (3, 4), (6, 3), (9, 2), (12, 1).