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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

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

Advanced Engineering Mathematics
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 14: Reflexive and Symmetric Relations** How many different reflexive, symmetric relations are there on the set \(\{a, b, c\}\)? **Options:** - ○ 10 - ○ none of these - ○ 6 - ○ 8 (Note: No graphs or diagrams are present in the image)
Transcribed Image Text:**Question 14: Reflexive and Symmetric Relations** How many different reflexive, symmetric relations are there on the set \(\{a, b, c\}\)? **Options:** - ○ 10 - ○ none of these - ○ 6 - ○ 8 (Note: No graphs or diagrams are present in the image)
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) ∈ R we have (b, a) ∈ R. Thus, we have: 32 - 32 = 9 - 32 = 3 choices

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

 

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