Let R1 be a partial order on X, and let R2 a partial order on Y. Let R be a relation on X x Y defined by: (x1, Y1) R (x2, Y2) → x1 R1 x2 ^ Yı R2 Y2- Show that R is a partial order on X × Y. Let S = {1,2, 3, ...}. Let R be a relation on he set S x S defined by (a, b) R (c, d) 2a – b = 2c – d. (i) Show that R is an equivalence relation. (ii) If S = {1,2, 3, 4, 5, 6, 7, 8}, find R[(2,5)], the equivalence class of (2,5).

Let R1 be a partial order on X, and let R2 a partial order on Y. Let R be a relation on X x Y defined by: (x1, Y1) R (x2, Y2) → x1 R1 x2 ^ Yı R2 Y2- Show that R is a partial order on X × Y. Let S = {1,2, 3, ...}. Let R be a relation on he set S x S defined by (a, b) R (c, d) 2a – b = 2c – d. (i) Show that R is an equivalence relation. (ii) If S = {1,2, 3, 4, 5, 6, 7, 8}, find R[(2,5)], the equivalence class of (2,5).

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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Question

Discrete structure

Let R1 be a partial order on X, and let R2 a partial order on Y. Let R be a relation
on X x Y defined by:
(x1, Y1) R (x2, Y2) → x1 R1 x2 ^ Yı R2 Y2-
Show that R is a partial order on X × Y.

Let S = {1,2, 3, ...}. Let R be a relation on he set S x S defined by
(a, b) R (c, d) 2a – b = 2c – d.
(i) Show that R is an equivalence relation.
(ii) If S = {1,2, 3, 4, 5, 6, 7, 8}, find R[(2,5)], the equivalence class of (2,5).

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Proof: R is a partial order.

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Further follows:

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Proof: R is an equivalence relation

VIEW

Equivalence class of (2,5):

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