Let A be a set with 10 distinct elements. i) How many binary relations on A are there? ii) How many of them are reflexive? iii) How many of them are symmetric? iv) How many of them are anti-symmetric relation?

Let A be a set with 10 distinct elements. i) How many binary relations on A are there? ii) How many of them are reflexive? iii) How many of them are symmetric? iv) How many of them are anti-symmetric relation?

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

Let A be a set with 10 distinct elements.

i) How many binary relations on A are there?
ii) How many of them are reflexive?
iii) How many of them are symmetric?
iv) How many of them are anti-symmetric relation?
v) How many of them are reflexive and symmetric?

(b) Show that a lattice is distributed if and only if for any elements a, b, c in the lattice

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