Question
The relation, $R=\{(1,3),(3,5)\}$ is defined on the set with minimum number of elements of natural numbers. The minimum number of elements to be included in $\mathrm{R}$ so that $\mathrm{R}$ is equivalence is(1) 5(2) 6(3) 7(4) 8
Step 1
We need to add the minimum number of elements to make this relation an equivalence relation. An equivalence relation is a relation that is reflexive, symmetric, and transitive. Show more…
Show all steps
Your feedback will help us improve your experience
Nidhi Singhi and 74 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Given the relation $\mathrm{R}=\{(1,3),(3,2)\}$ on the set of natural numbers, add minimum number of ordered pairs so that the enlarged relation is an equivalence relation.
Given the relation on $\mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{c})\}$ in the set $\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$ Then the minimum number of ordered pairs which added to $R$ make it an equivalence relation is (a) 5 (b) 6 (c) 7 (d) 8
Show that the relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3,4,5\}$ given by $\mathrm{R}=\{(a, b):|a-b|$ is even $\}$, is an equivalence relation. Show that all the elements of $\{1,3,5\}$ are related to each other and all the elements of $\{2,4\}$ are related to each other. But no element of $\{1,3,5\}$ is related to any element of $\{2,4\}$.
Relations and Functions
Introduction
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD