Prove that the (>) relation over the integers is total order in the theory of pa

Question

Prove that the (>) relation over the integers is total order in the theory of partial order. Prove that the (greaterthanorequalto) relation over the integers is partial order in the theory of total order. Show whether the following diagram is partial order or not. Suppose that R is the relation on the set of strings of English letters such that a R b if and only if length(a) = length(b). Is R an equivalence relation? Look at chapter 7 problems: 3, 4, and 6 Look at chapter 11 problems: 1, 2, 3, and 5

Explanation / Answer

2) A=N

where N= set of all integers

R is defined by xRy <-> x>Y

since a=a for all a E A

therefore aRa

: relation R is reflexive.

Suppose aRb and bRa -> a> and b>a

:a>b>a

relation R is anti symmetric.

suppose xRy and yRz->x>y and y>z

thereforex>z

:xRz

so relation R is transitive.

Hence A, R is a partial order set.

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