in Set Theory & Algebra edited by
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3 votes
3 votes

Given a set of values $\text{R} = \{1,2,3,4,5,6,7\}.$ The number of relations on this set which are both partial-order and equivalence relation is?

  1. $128$
  2. $1$
  3. $0$
  4. $2^{42}$
in Set Theory & Algebra edited by
639 views

2 Answers

5 votes
5 votes

Answer$: 1$

Let’s understand by taking base set $\text{R} = \{1,2,3,4\}.$

Given a set of values, suppose $\text{R} = \{1,2,3,4\}$ we need to find the number of relations on the set, which are both partial-order and equivalence relations.

1 vote
1 vote
$ R1= { (1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6) , (7,7) } $

Only above pair is common between both so ans = 1.
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