1 answer

10. (10 points) Define a relation on Z by setting x R y if xy is...

Question:

10. (10 points) Define a relation on Z by setting x R y if xy is even. a. Give a counterexample to show that is not reflexive

10. (10 points) Define a relation on Z by setting x R y if xy is even. a. Give a counterexample to show that is not reflexive. b. Give a counterexample to show that R is not transitive.

Answers

a) if x= 5 and y=5 then xy = 25 which is not even so x is not reflexive because it is not related to itself

b) let x,y,z = 3,4,5 respectively

x R y = xy = 3*4 =12 = even

y R z = yz = 4* 5= 20= even

xRz = xz = 3*5 = 15 which is not even

so its not transitive

.

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