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Question

If $A$ is a non-empty set, then which of the following is false?
$p blank colon$ Every reflexive relation is a symmetric relation
$q blank colon$ Every antisymmetric relation is reflexive
Which of the following is/are true?

(a) $p$ alone
$q$ alone
Both $p$ and $q$
Neither $p$ nor $q$

The correct answer is: Neither $p$ nor $q$

If $A equals open curly brackets 12 comma 3 close curly brackets comma$ then $R equals left curly bracket open parentheses 11 close parentheses comma open parentheses 22 close parentheses comma open parentheses 33 close parentheses comma left parenthesis 12 right parenthesis right curly bracket$ is reflexive on $A$ but it is not symmetric
So, a reflexive relation need not be symmetric
The relation ‘is less than’ on the set $Z$ of integers is antisymmetric but it is not reflexive

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