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Solution


Q.

Let A = {1, 2, 3, 4, 5, 6, 7}. Then the relation R={(x,y)∈A×A:x+y=7} is                     [2023]
1 an equivalence relation  
2 reflexive but neither symmetric nor transitive  
3 transitive but neither symmetric nor reflexive  
4 symmetric but neither reflexive nor transitive  

Ans.

(4)

Given, A={1,2,3,4,5,6,7}

and R={(x,y)∈A×A:x+y=7}

For Reflexive: Let y=x

So, x+x=7⇒x=72, which is not possible.

So, the given relation is not reflexive.

For Symmetric: xRy⇒x+y=7

⇒  y+x=7  ∴ xRy⇒yRx

Hence, the given relation is symmetric.

For Transitive: Let xRy and yRz⇒x+y=7 and y+z=7.

But it does not imply that x+z=7. 

So, R is not transitive.