30 Questions
What is true about the relation R defined by nRm ⇔ n is a factor of m?
R is reflexive but not symmetric
What is the minimum number of ordered pairs in a relation R on a finite set A having n elements?
Less than or equal to n
What is true about a relation R on a set A if (a, b) ∈ R and (b, a) ∈ R imply R = R^(-1)?
R is reflexive and symmetric
What is true about a relation R on a set A if nRp and mRp imply nRp?
R is transitive
What is true about a relation R on a set A if (a, b) ∈ R implies (b, a) ∈ R?
R is symmetric
What is a requirement for a relation R on a set A to be reflexive?
For every a in A, (a,a) is in R
What can be said about the identity relation on a non-void set A?
It is both reflexive and symmetric
What is the condition for a relation R on a set A to be symmetric?
For every a, b in A, if (a,b) is in R then (b,a) is in R
What is true about a reflexive relation on a set A?
It is not necessarily symmetric
What is the property of the universal relation on a non-void set A?
It is both reflexive and symmetric
What is the property of the identity relation on a set A?
It is reflexive and antisymmetric.
If a relation R on a set A is symmetric, then what can be said about the ordered pairs (a, b) and (b, a) in R?
They are always equal.
What is the condition for a relation R on a set A to be transitive?
For all a, b, c in A, aRb and bRc implies aRc.
What is the diagonal line of A × A?
The set of all ordered pairs (a, b) where a = b.
If R is a relation from A to B, which of the following is true about the domain of R?
The domain of R is a subset of A.
Let R be a relation from a set A to itself. If (a, b) ∈ R and (b, a) ∈ R imply (a, a) ∈ R, then what can be said about R?
R is symmetric and reflexive.
If R is the universal relation from A to B, which of the following is true about R?
R = A × B.
If a relation R on a set A is both symmetric and reflexive, then which of the following must be true?
R is its own inverse
Let R be a relation from a set A to itself. If for every a in A, (a, a) ∈ R, then what can be said about R?
R is reflexive but not symmetric.
Let R be a relation from a set A to itself. If for every a, b in A, (a, b) ∈ R implies (b, a) ∈ R, then what can be said about R?
R is symmetric but not reflexive.
What can be said about a relation R on a set A if R is reflexive and R is its own inverse?
R is symmetric but not antisymmetric
Let R be a relation on a set A such that R is symmetric and R is antisymmetric. What can be said about R?
R is a subset of the identity relation on A
If R is a reflexive relation on a set A, then which of the following must be true?
R is a superset of the identity relation on A
Let R be a relation on a set A such that R is the universal relation on A. What can be said about R?
R is both symmetric and reflexive
What can be said about the relation 'less than' in the set of natural numbers?
It is only transitive
Which of the following relations is always symmetric?
Identity relation
What is true about the inclusion of a subset in another, with reference to a universal set?
The relation is none of these
What is true about the relation R defined as {(2, 4), (4, 2), (4, 6), (6, 4)} on the set A = {2, 4, 6, 8}?
The relation is only symmetric
Which of the following statements is true about a reflexive relation R on a set A?
For every a in A, (a, a) ∈ R.
What is the condition for a relation R on a set A to be symmetric and antisymmetric?
(a, b) ∈ R implies (b, a) ∈ R and (a, a) ∉ R.
Determine the properties of a relation defined on the set of natural numbers. Identify if it is reflexive, symmetric, transitive, or an equivalence relation.
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