If a relation R on a set A is a partial order then which of the following need not be true?

R is transitive

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R is anti-symmetric

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R is symmetric

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R is reflexive

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Solution

The correct option is C R is symmetric
option (b)

A relation R on a set A is said to be a partial order is R is reflexive, anti-symmetric and transitive.

$∴$ R need not be symmetric.

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How many of the following statements are wrong

1. A relation is said to be reflexive on set A if each element in A is related to itself.

2. Empty relation defined on a non- empty set is reflexive

3. We can define a reflexive relation on A x B, where A is not a subset of B.

4. In a reflexive relation, all the elements should be of the form (a,a) for all a from the set on which the relation is defined

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