equivalence relation

A relation R is said to be circular if a R b and b R c together imply c R a. Which of the following options is/are correct?

Let $$S$$ be a set6 of $$n$$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $$S$$ are

Let R and S be any two equivalence relations on a non-emply set A. Which one of the following statements is TRUE?

(a) $$S = \left\{ { < 1,2 > ,\, < 2,1 > } \right\}$$ is binary relation on set $$A = \left\{ {1,2,3} \right\}$$. Is it irreflexive? Add the minimumnumber of ordered pairs to $$S$$...

Consider the following relations: $${R_1}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is even over the set of integers $${R_2}\,\,\left( {a,\,\,b} \right)\,\,\...

Suppose A = {a, b, c, d} and $${\Pi _1}$$ is the following partition of A $${\Pi _1}\, = \,\{ \{ a,\,\,b,\,\,c\,\} \,,\,\{ d\} \,\} $$ (a) List the ordered pairs of the equivalence...

Suppose $$A$$ is a finite set with $$n$$ elements. The number of elements in the Largest equivalence relation of $$A$$ is

Let $$R$$ be a symmetric and transitive relation on a set $$A$$. Then

State whether the following statement are TRUE or FALSE: (a) The union of two equivalence relations is also an equivalence relation.