Answered: 14. How many different relexive,…

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14. How many different relexive, symmetric relations are there on the set {a,b,c}? O 10 none of these 8

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

Expert Solution

Step 1

S = {a, b, c}

|S| = 3

Here the total possible relations are: 3² = 9

For the relation to be reflexive, we have the diagonal entries [(a, a), (b, b), (c, c)] of the table which can be chosen in only 1 way.

Now, for the symmetric relation whenever (a, b) $\in R$ we have (b, a) $\in R$ . Thus, we have: $\frac{3^{2} - 3}{2} = \frac{9 - 3}{2} = 3 choices$

So, we have 2³ ways of picking the pairs of distinct elements for symmetric relation.

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