1.Relations and Functions Quiz

What is an Empty Relation in a set A?

• No element of A is related to any element of A

• Each element of A is related to any element of A

• Some elements of A are related to each other

• All elements of A are related to each other

What is a Universal Relation in a set A?

• No element of A is related to any element of A

• Each element of A is related to any element of A

• Some elements of A are related to each other

• All elements of A are related to each other

What are the properties of an Equivalence Relation?

• Reflexive, symmetric and transitive

• Reflexive, antisymmetric and transitive

• Reflexive, symmetric and non-transitive

• Reflexive, non-symmetric and transitive

What is the property of a Reflexive relation?

• (b, a) € R, for every a, b € A

• (a, a) € R, for some a € A

• (a, b) € R, for every a, b € A

• (a, a) € R, for every a € A

What is the property of a Symmetric relation?

• (a, b) € R, for every a, b € A

• (a, a) € R, for every a € A

• (a1, a2) € R and (a2, a3) € R implies that (a1, a3) € R, for all a1, a2, a3 € A

• (a1, a2) € R and (a2, a1) € R, for all a1, a2 € A

What is the property of a Transitive relation?

• (a1, a2) € R and (a2, a1) € R, for all a1, a2 € A

• (a1, a2) € R and (a2, a3) € R implies that (a1, a3) € R, for all a1, a2, a3 € A

• (a, b) € R, for every a, b € A

• (a, a) € R, for every a € A

What is the property of a one-one (or injective) function?

• f(x1) = f(x2)

• f(x) = f(y)

• f(x) = y

• f(x) = x

What is the property of an onto (or surjective) function?

• f(x) = f(y)

• f(x) = x

• f(x) = y

• f(x1) = f(x2)

What is the property of a bijective function?

• f(x1) = f(x2)

• f(x) = y

• f(x) = f(y)

• f(x) = x

Which of the following is not a property of an Equivalence Relation?

• Reflexive

• Symmetric

• Transitive

• Antisymmetric