## sunainagupta Group Title Consider a set X = [2, 3, 4) and the Relation defined on X by. R = {(2, 2) (2, 3) (3, 3) (3, 4) (2, 4) (4, 4)}. Find whether R is : i) Reflexive ii) Symmetric iii) Transitive Also justify your answer. 10 months ago 10 months ago

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1. wio Group Title

Reflexive means: $\forall x \quad xRx$

2. wio Group Title

It's reflexive since it contains $$(2,2)$$, $$(3,3)$$, and $$(4,4)$$.

3. wio Group Title

Symmetric means: $\forall x\quad xRy\iff yRx$

4. wio Group Title

It's not symmetric because it contains $$(2,3)$$ but not $$(3,2)$$.

5. wio Group Title

@sunainagupta Are you following?

6. wio Group Title

Transitive means: $\forall x\quad xRy\wedge yRz\implies xRz$

7. wio Group Title

Let me rehash, since my notation was strange before. Reflexive $\forall x \quad (x,x)\in \mathcal{R}$ Symmetric $\forall x,y \quad (x,y)\in \mathcal{R} \iff (y,x)\in \mathcal{R}$ Transitive $\forall x,y,z \quad (x,y)\in \mathcal{R} \wedge (y,z)\in \mathcal{R} \implies (x,z)\in \mathcal{R}$

8. sunainagupta Group Title

thank you!

9. sunainagupta Group Title

A survey among the students of college. 60 Study Hindi, 40 study Spanish, and 45 study Japanese, Further 20 study Hindi and Spanish, 25 study Hindi and Japanese, 15 study Spanish and Japanese and 8 study all the languages. Find the followings: i) How many students are studying at least one language? ii) How many students are studying only Hindi ? iii) How many students are studying only Japanese ?