Question

A
Every mapping (function) is a relation but every relation is not a mapping.
B
The relation R is said to be reflexive if aRaaA (not for all)
C
The relation R is said to be symmetric if aRb then bRa. (not for all a and b)
D
The relation R is said to be transitive if aRb and bRc then aRc (not for all a,b,c)

Solution

## The correct options are B Every mapping (function) is a relation but every relation is not a mapping. C The relation $$R$$ is said to be symmetric if $$aRb$$ then $$bRa$$. (not for all $$a$$ and $$b$$) D The relation $$R$$ is said to be transitive if $$aRb$$ and $$bRc$$ then $$aRc$$ (not for all $$a,b,c$$)Every mapping (function) is a relation but every relation is not a mapping.The relation R is said to be reflexive if  $$\displaystyle a R a\forall a \epsilon A.$$(for all a$$\epsilon A$$)The relation R is said to be symmetric if $$aRb \Rightarrow bRa$$. (not for all a and b)The relation R is said to be transitive if $$aRb ; bRc \Rightarrow aRc$$ (not for all a,b,c)A relation from a set A to the set B is denoted as$$\displaystyle R= \left \{ \left ( x,y \right ):x \epsilon A\:and\:y \epsilon B\:and\:x R y \right \}$$$$\displaystyle \therefore R\subset A\times B.$$Mathematics

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