True or False (relation and functions)

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True or False (relation and functions)

Mathematics
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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 ? \(1.) \) \((a,a)\ \in \mathbb{N}\) \(2.) \) \((a,b)\ \in R \implies (b,a)\ \in R\) \(3.) \) \((a,b)\ \in R, (b,c)\ \in R\ \implies (a,c) \in R\)
is (5,5) in R?

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Other answers:

no
suppose (5,25) is in R, is (25,5) in R?
no
good. Try the last one
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
last one is false ?
yes it was written as \((a,a)\ \in \mathbb{N}\) for all \(a\ \in \mathbb{N}\) forgot to write that
good. So the first two are definitely false.
Typo. I meant to say if (25,5) is in R, then is (5,25) in R in part 2.
false
ok. You said part c is false? Can you give a counterexample?
(1,1) , (1,1) -> (1,1)
ok, but is true for ALL natural n?
no
well. (256, 16) and (16, 4) are both in R, but (256,4) is not in R
so false
yeah
ok thnx , it was easy i thought it was a way too hard

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