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  • The relation  <img alt="\dpi{100} \text { } R=\{(a, b): \operatorname{gcd}(a, b)=1,2 a \neq b, a, b \in Z\} \text { is : }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cdpi%7B100%7D

The relation  \dpi{100} \text { } R=\{(a, b): \operatorname{gcd}(a, b)=1,2 a \neq b, a, b \in Z\} \text { is : }

Option: 1

reflexive but not symmetric


Option: 2

transitive but not reflexive


Option: 3

symmetric but not transitive


Option: 4

neither symmetric nor transitive


Answers (1)

best_answer

\dpi{100} \begin{array}{ll} \operatorname{gcd}(a, b)=1, \quad 2 a \neq b & \\ { re\! f\! lexive\; gcd }\; (a, a)=a & \text { Not possible } \\ { symmetric\; gcd }\; (b, a)=1 \& 2 a \neq b & \text { Not possible } \\ a=2, b=1 & \end{array}                      

\! \! \!\! \! \! transitive\\ \\ \begin{array}{lll} (a, b)=(2,3) & \operatorname{gcd}\{a, b\}=1, & 2 \mathrm{a} \neq \mathrm{b} \\ (b, c)=(3,4) & \operatorname{gcd}\{c, d\}=1, & 2 \mathrm{a} \neq c \\ (a, c)=(2,4) & \operatorname{gcd}\{2,4\}=2, & 2 \mathrm{a}=c \end{array}

                                                                    \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; Not \; possible                                         

Posted by

Rakesh

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