Question

(Order is anti-symmetric) If a > b and b > a, then a = b. (e) a

Answer 1

a=b

Explanation:

An antisymmetric relation () satisfies the following property:

If (a, b) is in R and (b, a) is in R, then a = b.

This means that if a|b and b|a then a = b

If a|b then, b can be written as b = an for an integer n

If b|a then a can be written as a= bm for an integer m

Now we have b = (a)n = (bm)n

b = bmn

1 =mn

But since m and n are integers, the only two integers that satisfy this property would be m = n = 1

Therefore, b = an = a (1) = a ⇒b = a