Question

True or False (relation and functions)

Answer 1

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 ?

\(1.) \) \((a,a)\ \in \mathbb{N}\)


\(2.) \) \((a,b)\ \in R \implies (b,a)\ \in R\)


\(3.) \) \((a,b)\ \in R, (b,c)\ \in R\ \implies (a,c) \in R\)

Answer 2

@peachpi

Answer 3

is (5,5) in R?

Answer 4

no

Answer 5

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

Answer 6

no

Answer 7

good. Try the last one

Answer 8

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

Answer 9

last one is false ?

Answer 10

yes it was written as

\((a,a)\ \in \mathbb{N}\) for all \(a\ \in \mathbb{N}\)

forgot to write that

Answer 11

good. So the first two are definitely false.

Answer 12

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

Answer 13

false

Answer 14

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

Answer 15

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

Answer 16

ok, but is true for ALL natural n?

Answer 17

no

Answer 18

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

Answer 19

so false

Answer 20

yeah

Answer 21

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