Question

Choose the correct answer

• A. Every mapping (function) is a relation but every relation is not a mapping.
• B. The relation $R$ is said to be reflexive if $aRa\forall a\in A$ (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 $a,b,c$)

Answer 1

Answer: (A), (C), (D)

Every mapping (function) is a relation but every relation is not a mapping.
The relation $R$ is said to be symmetric if $aRb$ then $bRa$. (not for all $a$ and $b$)
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
$aRa\forall aϵA.$(for all a$ϵA$)
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
$R=\{(x,y):xϵAandyϵBandxRy\}$
$\therefore R\subset A\times B.$