The relation R=\{(a,b): (a,b)=1, 2a ≠ b, a,b {Z}\} is: [24-Jan-2023 Shift 1]

Correct Answer is : neither symmetric nor transitive

Correct Answer is : neither symmetric nor transitive

Test Index

Sets and Relations Part 1

Section: Mathematics

Question : 71 of 116

Marks: +1, -0

The relation

R=\{(a,b): \gcd(a,b)=1, 2a \neq b, a,b \in \mathbb{Z}\}

Solution:

Reflexive :

(a,a) \;\; \gcd

(a,a)=1

Which is not true for every a

E \mathbb{Z}

Symmetric:

Take

a=2, b=1 \;\; \gcd(2,1)=1

Also

2a=4 \neq b

Now when

a=1, b=2 \;\; \gcd(1,2)=1

Also now

2a=2=b

Hence

a=2 b

\Rightarrow R

is not Symmetric

Transitive:

Let

a=14, b=19, c=21

\gcd(a,b)=1

\gcd(b,c)=1

\gcd(a,c)=7

Hence not transitive

R

is neither symmetric nor transitive.

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