"Consider the following binary relations on the naturals (non-negative integers). Which onesare reexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify your claims.(a) A(x, y), dened to be true if and only if y is even.(b) B(x, y), dened to be true if and only if x < y.(c) C(x, y), dened to be true if and only if x + 2 y.(d) D(x, y), dened to be true if and only if x = y.(e) E(x, y), dened to be true if and only if the English name of x comes no later than thename of y in alphabetical order. (So, for example, E(8, 81) is true because eight comesbefore eighty-one, and E(8, 8) is true because eight comes no later than eight