Question

2. Which statement is an example of a transitive relationship? If ctm and m || n, then cin. If x = 2y and 2y 8, then x = 4. If a Il band b || c, then a || o. If min and mlp, then m || p.

Answer 1

A relationship is said to be transitive, if

a R b, b R c, then → a R c.

Test the given options

For the first option, if x = 2y and 2y = 8, then for transitive relationship,

`\begin{gathered} x=2y \\ 2y=8 \\ then,x=8 \end{gathered}`

the first option is not correct because x ≠ 4

For the second option, If a Il b and b || c, then a || c

`\begin{gathered} a\text{ R b means that a is parallel to b} \\ b\text{ R c means that b is parallel to c} \\ a\text{ R c means that a is parallel to c} \end{gathered}`

Looking at the second option, there is a relationship of parallelism between a, b and c, therefore, this is a transitive relationship

For the third option

If m ⊥ n and m ⊥ p, then m ∥​ p.

The statement from the point of view of transitive relationship is incorrect

it should be, n ⊥ p.