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Question

Set A={(x,y):x,yϵR,x2+y2=1}, B={x:xϵN,2x21<7}.
Are A and B comparable ?

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Solution

Given B={x:xN,2x21<7}
2x21<7
x24<0
x(2,2)
So, B={1} (since, -1,0 does not belongs to N)
Now, A={(x,y):x,yϵR,x2+y2=1}
x2+y2=1
which represents a circle.
There would be infinite points on the circle
A={(1,0)(0,1),(0,1),(1,0)....}

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