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?
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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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