equivalence relation - a collection R of ordered pairs of elements of x, satisfying certain properties. Write “x R y” to mean (x,y) is an element of R, and we say “x is related to y,” then the properties are:
1. Reflexive: a R a for all a Є R,
2. Symmetric: a R b implies that b R a for all a,b Є R
3. Transitive: a R b and b R c imply a R c for all a,b,c Є R.
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partial order- a collection R of ordered pairs of elements of x, satisfying certain properties. Write “x R y” to mean (x,y) is an element of R, and we say “x is related to y,” then the properties are:
1. Reflexive: a R a for all a Є R,
2. Anti-Symmetric: a R b and b R a implies that for all a,b Є R
3. Transitive: a R b and b R c imply a R c for all a,b,c Є R.
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total order - a collection R of ordered pairs of elements of x, satisfying certain properties. Write “x R y” to mean (x,y) is an element of R, and we say “x is related to y,” then the properties are:
1. Reflexive: a R a for all a Є R,
2. Symmetric: a R b implies that b R a for all a,b Є R
3. Transitive: a R b and b R c imply a R c for all a,b,c Є R.
4. Comparability : either a R b or b R a for all a,b Є R.
so correct option is A
So R is not reflexive.
∴R is neither a partial order, nor an equivalent relation.