## mathmath333 one year ago True or False (relation and functions)

1. mathmath333

let $$\large R$$ be a relation from $$\large \mathbb{N}$$ to $$\large \mathbb{N}$$ defined by \large \color{black}{\begin{align} R=\{(a,b):a,b \ \in \mathbb{N} \ \text{and} \ a=b^2 \} \hspace{.33em}\\~\\ \end{align}} are the following true ? $$1.)$$ $$(a,a)\ \in \mathbb{N}$$ $$2.)$$ $$(a,b)\ \in R \implies (b,a)\ \in R$$ $$3.)$$ $$(a,b)\ \in R, (b,c)\ \in R\ \implies (a,c) \in R$$

2. mathmath333

@peachpi

3. anonymous

is (5,5) in R?

4. mathmath333

no

5. anonymous

suppose (5,25) is in R, is (25,5) in R?

6. mathmath333

no

7. anonymous

good. Try the last one

8. anonymous

Btw, i'm assuming the questions means *for all natural n*. The first one is true if a = 1 and b = 1 but not true for other natural

9. mathmath333

last one is false ?

10. mathmath333

yes it was written as $$(a,a)\ \in \mathbb{N}$$ for all $$a\ \in \mathbb{N}$$ forgot to write that

11. anonymous

good. So the first two are definitely false.

12. anonymous

Typo. I meant to say if (25,5) is in R, then is (5,25) in R in part 2.

13. mathmath333

false

14. anonymous

ok. You said part c is false? Can you give a counterexample?

15. mathmath333

(1,1) , (1,1) -> (1,1)

16. anonymous

ok, but is true for ALL natural n?

17. mathmath333

no

18. anonymous

well. (256, 16) and (16, 4) are both in R, but (256,4) is not in R

19. mathmath333

so false

20. anonymous

yeah

21. mathmath333

ok thnx , it was easy i thought it was a way too hard