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Question

Choose the correct answer 


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