DM - Functions & Relations -Q9

+2 votes

Let A = \{1,2,3,4,5,6,7\} The number of symmetric relations on set A which contains exactly 4 elements?

asked Jun 24 in Discrete Maths by gbeditor (44,500 points)
reshown 6 days ago by gbeditor

1 Answer

+1 vote
 
Best answer
a=[1,2,3,4,5,6,7]

a*a={(1,1),(2,2),(3,3).................................(7,7),  (1,2)(2,1)  (1,3)(3,1)...............................................................}

no of diagonal elements=7

no of non diagonal elements=42

now since it is symmetric relation we will take all the elements like (a,b) and (b,a) into pairs. so no of pairs in above question will be =42/2=21

now remember each pair contain two elements

now in symmetric relation diagonal elements can be there in any order or any number of times.

ATQ we have to form the relations with elements 4

so let take the cases:

case 1: there are no diagonal elements and 2 pairs     7c0 * 21c2= 210

case 2: there are  two diagonal elements and 1 pair    7c2 * 21c1=441

case 3: there are 4 diagonal elements and 0 pair    7c4* 21c0 = 35

total=210+441+35=686
answered 4 days ago by deepak-gatebook (112,390 points)
Answer:
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