## sunainagupta one year ago 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.

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1. wio

Reflexive means: $\forall x \quad xRx$

2. wio

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

3. wio

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

4. wio

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

5. wio

@sunainagupta Are you following?

6. wio

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

7. wio

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

thank you!

9. sunainagupta

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 ?