10.2.13 - INFS 501 10.2.13 Consider the circle relation x y...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
INFS 501 10.2.13 Consider the circle relation x, y ∈ℝ , x C y x 2 y 2 = 1. Remember we may use the alternative notation, x,y ∈ C, instead of xCy. Is C Reflexive? Answer : No, C is not reflexive. For example, 0 2 0 2 = 0 1, so 0,0  ∉ C. For another example, 15 2 15 2 = 450 1, so 15,15  ∉ C. (It takes only one counterexample to prove C is not reflexive.) Is C Symmetric? Answer : Yes, C is symmetric. If x,y ∈ ℝ and x,y  ∈ C, so x 2 y 2 = 1, then necessarily, by the commutative law of addition, y 2 x 2 = 1, and therefore
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online