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