JNU exam

Question

If R be an equivalence relation on the set, A={6,7,8,9,10} defined by,

R={(6,6),(7,7),(8,8),(9,9),(10,10),(6,7),(7,6),(8,9),(9,8),(9,10),(10,9),(8,10),(10,8)}, its partitions are

a) {{6},{7},{8,9},{10}}

b) {{6,7,8},{9,10}}

c) {{6},{7,8},{9,10}}

d) {{6,7},{8,9,10}}

Answer 1

do the partitionn of any set like.......1.none of the subset having common {non empty disjoint }

2.on combine them actual set should be formed.

and partition of equivalence relation be like..........see how the set elements are relateed with each other

first partition= 6 is related to 6 and 7.........so {6,7}

similarly  2nd =7 is related to 7 and 6 so................. {7,6}
......3rd=..................................................................{8,9,10}

......4th=.................................................................{9,8,10}

........5th=..............................................................{10,9,8}

1st nd 2nd r equivalent

3rd 4th 5th are same..

so only option  d is corret

Comments

Actually we can say transitivity property satisfies for (8,9,10)

which not satisfies for 6,7