1.R on N defined by:mRn iff m>10n 2. R on Z defined by:mRn iff m+n is even 3. R

Question

1.R on N defined by:mRn iff m>10n
2. R on Z defined by:mRn iff m+n is even
3. R on Z defined by:mRn iff m-n is even
4. E on r defined by:xEy iff y=e^x
5. R on R defined by:xRy iff xy=0

6. S on the set,T, of all triangles in a plane defined by t_1St_2 iff t_1 and t_2 are similar

7. perpendicularity on the set,L, of all straight lines in the plane

8. R with the domain R and the codomain the set,P, of all real polynomials in one unknown, defined by aRp iff a is a root of p

9. R on the set PXL, where P is the set of all points in the plane,L is the set of all straight lines in the plane, and pRl means that the point p lies on the line l

10. P on the set,A, of all people, where xPy means x is a parent of y

11. S on the set of all Americans where aSb means a is a sibling of b

12. B on the set of all Americans where aBb means a is a brother of b

13. R on the set R defined by xRy iff(x<0) or(x=0 and x=y)

give three further examples of relations where the domain and codomain are different

Explanation / Answer

a) R on N defined by: xRy iff x< -100y b) R on R defined by : xRy -> x = sin y c) K on set of all mammals , where aKb means 'a' has a tail('b')

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