Example: Let R be the relation on the set of people such that x R y if x and y are people and x is older than y. Show that R is not a partial ordering.
{"Image DocumentName": "Example: Let R be the relation on the set of people such that x R y if x and y are people and x is older than y. Show that R is not a partial ordering.", "Image ImageDescription": "Solution: R is anti-symmetric because if a person x is older than a person y, then y is not older than x. That is if (x,y) \u03f5 R, then (y,x)\u2209 R is not possible. R is transitive because if a person x is older than person y and y is older then person z, then x is older then z. that is , x R y and y R z, then x R z. However, R is not reflexive, because no person is older than himself or herself. That is, (x,x) \u2209 R for all people x. it follows that R is not a partial ordering and poset.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}