The relation R ={( a , b ): operatorname{gcd} | vedclass

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Question

Reflexive : $(a, a) \Rightarrow \operatorname{gcd}$ of $(a, a)=1$

Which is not true for every a $\epsilon Z$.

Symmetric:

Take $a =2, b =1 \Ri

Vedclass · Accepted Answer

neither symmetric nor transitive

Vedclass · Answer

Reflexive : $(a, a) \Rightarrow \operatorname{gcd}$ of $(a, a)=1$

Which is not true for every a $\epsilon Z$.

Symmetric:

Take $a =2, b =1 \Rightarrow \operatorname{gcd}(2,1)=1$

Also $2 a=4 
eq b$

Now when $a =1, b =2 \Rightarrow \operatorname{gcd}(1,2)=1$

Also now $2 a =2= b$

Hence $a=2 b$

$\Rightarrow R$ is not Symmetric

Transitive:

Let $a =14, b =19, c =21$

$\operatorname{gcd}( a , b )=1$

$\operatorname{gcd}(b, c)=1$

$\operatorname{gcd}( a , c )=7$

Hence not transitive

$\Rightarrow R$ is neither symmetric nor transitive.

The relation $R =\{( a , b ): \operatorname{gcd}( a , b )=1,2 a \neq b , a , b \in Z \}$ is:

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