The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is __________Question 1Answerreflexive, symmetric and transitiveneither reflexive, nor irreflexive but transitiveirreflexive and antisymmetricirreflexive, symmetric and transitive
Question
The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is __________Question 1Answerreflexive, symmetric and transitiveneither reflexive, nor irreflexive but transitiveirreflexive and antisymmetricirreflexive, symmetric and transitive
Solution
The binary relation is neither reflexive, nor irreflexive but transitive.
Here's why:
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Reflexivity: A relation is reflexive if every element is related to itself. In this case, (1,1) and (2,2) are present, but (3,3) is not. So, it's not reflexive.
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Irreflexivity: A relation is irreflexive if no element is related to itself. In this case, (1,1) and (2,2) are present, so it's not irreflexive.
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Transitivity: A relation is transitive if whenever an element a is related to an element b, and b is related to an element c, then a is also related to c. In this case, for example, we have (2,1) and (1,1), so we would need (2,1) to be transitive, and it is. All other pairs also meet this requirement, so the relation is transitive.
Therefore, the relation is neither reflexive, nor irreflexive but transitive.
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