Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Let N be the set of natural numbers and R be the relation on  defined by (a, b) R (c, d) iff ad = bc for all a, b, c, d <img alt="\in" src="https://learn.care

Let N be the set of natural numbers and R be the relation on N \times N defined by (a, b) R (c, d) iff ad = bc for all a, b, c, d \in N. Show that R is an equivalence relation.

 

 

Answers (1)

\\ $ Reflexive: $ \\ $ (a, b) $ \in \mathrm{N} \times \mathrm{N} \\ a \cdot b=b \cdot a \\ \Rightarrow (a, b) R(a, b) \\ $ R is reflexive $ \\\\ $ Symmetric: $ \\ $ (a, b),(c, d) $ \in N \times N \\ $ (a, b) R(c, d) $ \Rightarrow a \cdot d=b \cdot c \\ \mathrm{c} \cdot \mathrm{b}=\mathrm{d} \cdot \mathrm{a} \\ \Rightarrow(\mathrm{c}, \mathrm{d}) \mathrm{R}(\mathrm{a}, \mathrm{b}) \\ \mathrm{R} \text { is symmetric } \\\\ $ Transitive:$ \\ (a, b),(c, d),(e, f), $ \in N \times N \\ $(a, b) R(c, d)$ \& $(c, d) R(e, f)$ \Rightarrow a \cdot d=b \cdot c \ \& \ c \cdot f=d \cdot e \\ a \cdot d \cdot c \cdot f=b \cdot c \cdot d \cdot e \Rightarrow a \cdot f=b \cdot e \\ (a, b) R(e, f)\\ R \text { is transitive } \\ $ \quad \mathrm{R} $ is reflexive , symmetric and transitive. Hence R is an equivalance relation

Posted by

Safeer PP

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE admit card 2025 out for Class 10, 12 supplementary exams
anam-khan

CBSE Class 10, 12 practical exams 2025 for compartment students from July 10; detailed guidelines issued
anam-khan

CBSE Central Sector Scheme of Scholarship 2025 applications open on scholarships.gov.in

Latest Question