WorksheetsRelations in Mathematics Quiz
Total questions: 20
Worksheet time: 10mins
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
Which of the following relations is reflexive on the set of integers?
Divides
Greater than
Equal to
Less than
A relation R is called irreflexive if:
aRa for all a in the set
aRb implies b does not relate to a
aRa for no a in the set
aRa for some a in the set
If R is a relation on set A, and S is a relation on set B, the composition of R and S is:
A relation from A to B
A relation from A to A
A relation from B to B
A relation from A to B and B to A
In a directed graph, a relation is represented by:
Vertices
Edges
Paths
Cycles
Which of the following relations is not an equivalence relation?
The "equal to" relation on integers
The "congruence modulo n" relation
The "divides" relation on integers
The "parallel to" relation on lines
Which of the following properties is required for a relation to be antisymmetric?
aRb implies bRa
aRb and bRa implies a = b
aRb implies b ≠ a
aRa for all a in the set
If a relation R is both symmetric and antisymmetric, then it must be:
Reflexive
Irreflexive
Transitive
Both reflexive and irreflexive
A relation on a set of people defined by "is a sibling of" is:
Reflexive
Symmetric
Transitive
Antisymmetric
The relation R on the set of natural numbers, defined by "x divides y," is:
Reflexive and symmetric
Reflexive and antisymmetric
Symmetric and transitive
Irreflexive and transitive
Which of the following is a symmetric relation but not transitive?
The "friendship" relation
The "greater than" relation
The "divides" relation
The "congruence modulo n"
