5 Suppose A and B are sets and R is a relation from A to B. For each b E B define the horizontal section of R at b by H₁ = {a e A: aRb}. Prove that U{H,: bE B} is the domain of R. 6 Suppose A and B are sets and R is a relation from A to B. For each a E A define the vertical section of R at a by Va = {be B: aRb}. Prove that U{Va: a € A} is the range of R. In the above two problems how are the vertical and horizontal sections of R and R ¹ related?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.4: Relationships: Perpendicular Lines
Problem 17E: Does the relation is a brother of have a reflexive property consider one male? A symmetric property...
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Please Prove these step by step and use language that would be used in proofs ie: Thus. Therefore. By definition x

5 Suppose A and B are sets and R is a relation from A to B. For each b E B define
the horizontal section of R at b by H = {a e A: aRb}. Prove that U{H,: b = B}
is the domain of R.
6 Suppose A and B are sets and R is a relation from A to B. For each a € A define
the vertical section of R at a by Va = {be B: aRb}. Prove that U{Va: a € A} is
the range of R.
In the above two problems how are the vertical and horizontal sections of R and R ¹
related?
Transcribed Image Text:5 Suppose A and B are sets and R is a relation from A to B. For each b E B define the horizontal section of R at b by H = {a e A: aRb}. Prove that U{H,: b = B} is the domain of R. 6 Suppose A and B are sets and R is a relation from A to B. For each a € A define the vertical section of R at a by Va = {be B: aRb}. Prove that U{Va: a € A} is the range of R. In the above two problems how are the vertical and horizontal sections of R and R ¹ related?
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