Relations in Mathematics Quiz

A relation is defined as:

• a subset of the Cartesian product of two sets

• The union of two sets

• The difference of two sets

• A set of ordered pairs

Which of the following is an equivalence relation?

• Reflexive, Symmetric, Transitive

• Asymmetric, Antisymmetric

• Irreflexive, Symmetric, Transitive

• Reflexive, Symmetric, Asymmetric

A relation R is said to be reflexive if:

• aRb implies bRa

• aRa for all a in the set

• aRb implies b does not relate to a

• aRb for all a and b in the set

Which of the following relations is symmetric?

• Less than

• Divides

• Equality

• Greater than

Which of the following is a transitive relation?

• a < b and b < c implies a < c

• a = b and b = c implies a ≠ c

• a ≤ b and b ≤ c implies a ≥ c

• a ≠ b and b ≠ c implies a ≠ c

A relation is called antisymmetric if:

• aRb implies b does not relate to a

• aRb implies bRa

• aRb and bRa implies a = b

• aRb implies a ≠ b

The relation "less than" (<) on the set of integers is:

• Reflexive and symmetric

• Antisymmetric and transitive

• Symmetric and transitive

• Reflexive and antisymmetric

Which of the following is true for a relation R that is both symmetric and transitive?

• It must be reflexive

• It must be irreflexive

• It cannot be antisymmetric

• It is an equivalence relation if it is also reflexive

A relation R on a set is said to be an equivalence relation if it is:

• Reflexive, irreflexive, and symmetric

• Reflexive, symmetric, and transitive

• Symmetric, antisymmetric, and irreflexive

• Transitive, symmetric, and irreflexive

If R is a relation on a set A, then the inverse relation R⁻¹ is:

• The set of pairs (a, b) where bRa

• The set of pairs (a, b) where aRb

• The set of pairs (a, a) where a ∈ A

• None of the above