Question #309374

Let R1 and R2 be two relation on real number such that R1 = {(x, y)|x < y} and R2 =

{(x, y)|x > y}, then find R1 ∪ R2,R1 ∩ R2,R1 − R2, R2 − R1, and R1+LR2.

1
Expert's answer
2022-03-16T05:08:06-0400

R1\cup R2={(x,y)|x>y or x<y}={(x,y)|x!=y}

R1\cap R2={(x,y)|x>y and x<y}=\varnothing

R1-R2=R1-R1\cap R2=R1 -{(x,y)|x>y and x<y}=R1-\varnothing=R1

R2-R1=R2-R1\cap R2=R2 -{(x,y)|x>y and x<y}=R2-\varnothing=R2

R1+LR2=R1\cup LR2-R1\cap LR2={(х,у)xR,yR|\forall x \in\R,\forall y \in \R}-∅={(x,y)xR,yR|\forall x \in\R,\forall y \in \R }


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