Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be representedas (r, y) ry = 1} . Use a similar representation for each of your answers to the questionsbelow, and write your answer in the accompanying boxWhat is the composite relation R2 ?(a)(b)What is the composite relation R3?What is the composite relation R4?(c)(d)What is the transitive closure of R?

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Asked Dec 4, 2019
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Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented
as (r, y) ry = 1} . Use a similar representation for each of your answers to the questions
below, and write your answer in the accompanying box
What is the composite relation R2 ?
(a)
(b)
What is the composite relation R3?
What is the composite relation R4?
(c)
(d)
What is the transitive closure of R?
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Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r, y) ry = 1} . Use a similar representation for each of your answers to the questions below, and write your answer in the accompanying box What is the composite relation R2 ? (a) (b) What is the composite relation R3? What is the composite relation R4? (c) (d) What is the transitive closure of R?

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Expert Answer

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Step 1

(a) Obtain the composite relation as follows.

The composition of relations R: A >B and S : B ->C is given by
_
R and (b.c) eC}
RoS-{a.c) a A.c e C such that (a.b)
R={(x, y)xy
R2
= RoR
{(x, y): xy=1o{x, y): xy - 1}
1
x =x and y
1
and y x
{(xr, y): x= y}
X=_
=_
11
х
х
help_outline

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The composition of relations R: A >B and S : B ->C is given by _ R and (b.c) eC} RoS-{a.c) a A.c e C such that (a.b) R={(x, y)xy R2 = RoR {(x, y): xy=1o{x, y): xy - 1} 1 x =x and y 1 and y x {(xr, y): x= y} X=_ =_ 11 х х

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Step 2

(b) Obtain the composite relation as follows.

R= {(x, y):xy = 1}
R² = {(x.y) :x = y}
ху
R
= R? • R
= {(x, y):x= y}•{(x.y):xy =1}
х,
|{(x.y): xy = 1}| [x = x and y = x]^ x =x and y
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R= {(x, y):xy = 1} R² = {(x.y) :x = y} ху R = R? • R = {(x, y):x= y}•{(x.y):xy =1} х, |{(x.y): xy = 1}| [x = x and y = x]^ x =x and y

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Step 3

(c) Obtain the composite r...

R ={(x,y) xyl}
-{(x, y) sy = 1}
= R3 o R
-{x, y): ay-1o{(x, y) xy=1}
{ x. y):x= y}
1
and y x
x =x and y
X=_
help_outline

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R ={(x,y) xyl} -{(x, y) sy = 1} = R3 o R -{x, y): ay-1o{(x, y) xy=1} { x. y):x= y} 1 and y x x =x and y X=_

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Advanced Math