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2. For each relation on Z, determine if it one-to-one, one-to-many, many-to-one, or many-to-many and identify the properties of it. d) ρ={(1, 1), (2,2),(1,4), (3,2), (2,3), (4,1), (3,3))
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Answer #1

(a)

x ho yleftrightarrow |x|= y

The relation is many to one as | -x | = | x |

(b)

x ho yleftrightarrow2 |(x+ y)

2 divides (x+y) means the relation is many to many.

Because all odd numbers are related to each other and all even numbers are related to each other.

(c)

x ho yleftrightarrow x= y^2

The relation is one to many.

Because (-y)2= y2

(d)

ρ一{(1.1).(2. 2).(1.4). (3, 2). (2.3). (4.1). (3.3)}

The relation is many to many.

as (1,1) and (1,4)

and (2,2) and (3,3) are in relation.

(e)

x ho y= x le y

The relation is many to many.

as x is related to x, x+1, ......, infty

and y is related to y, y-1, y-2, ....,-infty

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