total number of equivalence relation on S={a,b,c}

Asked by Dharvi Kumra | 26th Apr, 2015, 07:13: PM

Expert Answer:

L e t space S equals open curly brackets a comma b comma c close curly brackets T h e n space t h e space p o s s i b l e space e q u i v a l e n c e space r e l a t i o n s space a r e open curly brackets open parentheses a comma a close parentheses comma open parentheses b comma b close parentheses comma open parentheses c comma c close parentheses comma open parentheses a comma b close parentheses comma open parentheses b comma a close parentheses comma open parentheses c comma b close parentheses comma open parentheses b comma c close parentheses comma open parentheses c comma a close parentheses comma open parentheses a comma c close parentheses close curly brackets comma space open curly brackets open parentheses a comma a close parentheses comma open parentheses b comma b close parentheses comma open parentheses c comma c close parentheses comma open parentheses a comma b close parentheses comma open parentheses b comma a close parentheses close curly brackets comma space open curly brackets open parentheses a comma a close parentheses comma open parentheses b comma b close parentheses comma open parentheses c comma c close parentheses comma open parentheses c comma a close parentheses comma open parentheses a comma c close parentheses close curly brackets comma space open curly brackets open parentheses a comma a close parentheses comma open parentheses b comma b close parentheses comma open parentheses c comma c close parentheses comma open parentheses c comma b close parentheses comma open parentheses b comma c close parentheses close curly brackets comma open curly brackets open parentheses a comma a close parentheses comma open parentheses b comma b close parentheses comma open parentheses c comma c close parentheses close curly brackets T h u s comma space t h e r e space a r e space f i v e space e q u i v a l e n c e space r e l a t i o n s space o n space S.

Answered by Vimala Ramamurthy | 27th Apr, 2015, 11:52: AM