Question
On the set S of all real numbers, define a relation . Show that R is reflexive.
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Text solutionVerified
Given,
Reflexive Property
The Reflexive Property states that for every real number x, .
when,
So, is possible, and is also possible as . and .
Symmetric Property
The Symmetric Property states that for all real numbers x and y,
if , then .
Transitive Property
The Transitive Property states that for all real numbers x ,y, and z,
if and , then
Therefore, R is reflexive
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Question Text | On the set S of all real numbers, define a relation . Show that R is reflexive. |
Answer Type | Text solution:1 |
Upvotes | 150 |