Question

Determine whether the binary relation R on {a, b, c}   where R={(a, a), (b, b)), (c, c), (a, b), (a, c), (c, b) } is:

	a.	reflexive, antisymmetric, symmetric
	b.	transitive, symmetric, antisymmetric
	c.	antisymmetric, reflexive, transitive
	d.	symmetric, reflexive, transitive

Answer 1

The Relation R={(a, a), (b, b)), (c, c), (a, b), (a, c), (c, b) } the binary relation has following property:

The relation R is reflexive as it has (a,a) (b,b) and (c,c),

It is also transitive as it has (a,b), (a,c), and (c,b)

It is antisymmetric as it does not have (b,a) for (a,b).

So, the relation R has the following property, it is reflexive, anti-symmetric, and transitive.

So, option C is the correct answer.

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