Given any partial order P , we can form its sym metric closure P8 by taking the union of P and p - 1 . (a) Explain why P8 is reflexive and symmetric. (b) Given an example of a partial order P such that P8 is not an equivalence relation. (c) Give an example of such a P that also has the property from Problem 2.10.8. ( d) Prove that if P is a linear order, then P8 is an equivalence relation. ( e) Can you find an example of a P that is not a linear order, where P8 is an equivalence relation

Need with son's homework i will give 30 ! show work daniel's house is located b miles from his school. the swimming pool is 3 miles farther from his school. his dr. office is 4 miles less than twice the distance from home to daniel's school. a. write an expression that shows the distance from daniel's house to the swimming pool. b. write an expression that shows the distance from daniel's house to his dr's office c. if b=3, is the swimming pool or dr's office closer to daniel's house? how much closer