Let S 3k 1 k w Show that for all x y S we have xy SSolutio

Let S = {3k +1 : k w}. Show that for all x, y S, we have xy S.

Solution

As, We know w is whole number which means w={0,1,2,3,.......... }

Suppose,

Let us take one example,

x = 3k+1, when k=2, k w

x=3(2)+1 = 7

Therefore, x S

y= 3k+1 , when k=4, k w

y=3(4)+1

y=13

Therefore, y S

Now, xy = (7).(13) = 91,

which means 91 S

Therefore, we conclude that xy S