Question

Express the relation in Roaster form: R=(x,y):y+2x=5,x,yEW}

Answer 1

Answer:

roaster form is given for the given set

Answer 2

Correct question: Express the relation in Roster form: R = {(x, y) : y+2x = 5 , x, y ∈ W}.

Answer:

The roster form of the relation will be R  = {(0,5), (1,3), (2,1)}

Given,

The relation R = {(x, y) : y+2x = 5 , x, y ∈ W}.

To Find,

The roster form of the relation.

Solution,

The method of finding the roster form of the relation is as follows -

We know that the set W represents the set of whole numbers i.e. a set containing the positive integers and zero.

Now we need to find the pairs of (x, y) where x, y ∈ W and the values of x and y satisfy the equation $y+2x = 5$ .

Now if we put x = 0, we get $y+2*0=5$  ⇒  $y=5$. So in this case, (x, y) = (0,5).

If we put x = 1, we get $y+2*1=5$ ⇒ $y+2=5$ ⇒ $y=5-2=3$. So in this case, (x, y) = (1, 3).

If we put x = 2, we get $y+2*2=5$ ⇒ $y+4=5$ ⇒ $y=5-4=1$. So in this case, (x, y) = (2,1).

But if we put x = 3, we get $y+2*3=5$ ⇒ $y+6=5$  ⇒  $y=5-6=-1$, which is not a whole number.

In this way, if we try to put any whole number greater than 2 in the place of x, the value of y will not remain a whole number.

So only the pairs (0,5), (1,3), and (2,1) will satisfy the conditions.

Hence, the roster form of the relation will be R  = {(0,5), (1,3), (2,1)}

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