# 4.4.6 Determine if the following relations are reflexive, irreflexive other(a) The relation x < y on the set Z.(b) The relation "x is married to y" with domain and codomain the aof all people in the USA(c) The relation r= { (x, y) e N x N: x-y = 1 }.Scanned withCSCamSca (d)eThe relation r2 ={(3, 4), (4,4), (2, 3), (3, 3), (1,2), (2,1), (4,3).

Question
14 views help_outlineImage Transcriptionclose4.4.6 Determine if the following relations are reflexive, irreflexive o ther (a) The relation x < y on the set Z. (b) The relation "x is married to y" with domain and codomain the a of all people in the USA (c) The relation r= { (x, y) e N x N: x-y = 1 }. Scanned with CS CamSca (d)eThe relation r2 = {(3, 4), (4,4), (2, 3), (3, 3), (1,2), (2,1), (4,3). fullscreen
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Step 1

According to the given information it is required to check whether the relation is reflexive, irreflexive or neither.

A binary relation R over the set X is reflexive if every element of X is related to itself.

And

A binary relation R over the set X is irreflexive if it does not relate any element to itself.

For part (a)

The relation x < y on the set Z

There is no element belong to Z such that x < x so, the relation is irreflexive as no element relate to itself.

Step 2

For part (b)

The relation x is married to y with domain and codomain the set of all people in USA

It is not possible that any person can marry to itself so, the relation is irreflexive as no element relate to itself.

Step 3

For part (...

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