Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ ans. symmetric transitive reflexive reflexive and transitive
Question
Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ ans. symmetric
transitive
reflexive
reflexive and transitive
Solution
The correct answer is "reflexive and transitive".
In a partially ordered set (also known as a poset), the relation R is reflexive, antisymmetric, and transitive.
-
Reflexive: This means for every element 'a' in set A, the relation aRa holds true. In simpler terms, every element is related to itself.
-
Transitive: This means if aRb and bRc, then aRc. In simpler terms, if an element 'a' is related to an element 'b', and 'b' is related to an element 'c', then 'a' is also related to 'c'.
The relation is not necessarily symmetric in a poset. Symmetric means if aRb then bRa, which is not required in a poset.
So, the relation R in a poset is reflexive and transitive, but not necessarily symmetric.
Similar Questions
Assume the R is a relation on a set A, aRb is partially ordered such that a and b
n the set N×N, the relation R is defined by (a, b) R(c,d)⇔ad=bc. Then R ispartial order relationequivalence relationreflexive and transitive but not symmetricsymmetric and transitive but not reflexive
A={1,2,3,4}, THEN R={(1,2),(1,3),(3,3),(3,1)} IS A __________ans.TRANSITIVE RELATIONNON SYMMETRIC RELATIONANTI SYMMETRIC RELATIONREFLEXIVE RELATION
Determine if R is reflexive, symmetric, transitive.. Group of answer choicesTransitivenone of the aboveSymmetricReflexive
Let R be a relation defined on N as a R b is 2a+3b is a multiple of 5,a,b∈N. Then R isnot reflexivetransitive but not symmetricsymmetric but not transitivean equivalence relation
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.