Pls Help 2. Consider the relation S × S of all ordered pairs of elements of S, w

Question

Pls Help

2. Consider the relation S × S of all ordered pairs of elements of S, where S is non-empty Which of the following properties does this relation have a) Reflexive b) Irreflexive c) Symmetric d) Antisymmetric e) Transitive f) Partial order relation g) Equivalence relation 3. Which of the following properties will be true on the union RUS of two relations if they are true on R and S individually? a) Reflexivie b) Irreflexive c) Symmetric d) Antisymmetric e) Transitive f) Partial order relation g) Equivalence relation

Explanation / Answer

Answer:

2. Equivalence relation, as for a Cartesian product all 3 properties, Reflexive, symmetric and transitive Holds, so it will be Equivalence Relation.

3. A and C, as it will be Symmetric and reflexive but not transitive, also anti symmetry , Irreflexive and transitivity are not trivial in case of union or any other operation on a set.

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