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Computer-Networks
October 4, 2023
Operating-Systems
October 4, 2023
Computer-Networks
October 4, 2023
Operating-Systems
October 4, 2023

UGC NET CS 2016 July- paper-2

Question 1
How many different equivalence relations with exactly three different equivalence classes are there on a set with five elements?
A
10
B
15
C
25
D
30
Question 1 Explanation: 
Step-1: Given number of equivalence classes with 5 elements with three elements in each class will be 1,2,2 (or) 2,1,2 (or) 2,2,1 and 3,1,1.
Step-2: The number of combinations for three equivalence classes are
2,2,1 chosen in (​ 5​ C​ 2​ *​ 3​ C​ 2​ *​ 1​ C​ 1​ )/2! = 15
3,1,1 chosen in(​ 5​ C​ 2​ *​ 3​ C​ 2​ *​ 1​ C​ 1​ )/2! = 10
Step-3: Total differential classes are 15+10
=25.
Correct Answer: C
Question 1 Explanation: 
Step-1: Given number of equivalence classes with 5 elements with three elements in each class will be 1,2,2 (or) 2,1,2 (or) 2,2,1 and 3,1,1.
Step-2: The number of combinations for three equivalence classes are
2,2,1 chosen in (​ 5​ C​ 2​ *​ 3​ C​ 2​ *​ 1​ C​ 1​ )/2! = 15
3,1,1 chosen in(​ 5​ C​ 2​ *​ 3​ C​ 2​ *​ 1​ C​ 1​ )/2! = 10
Step-3: Total differential classes are 15+10
=25.
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