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mathmath333

  • one year ago

True or False (relation and functions)

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  1. mathmath333
    • one year ago
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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 ? \(1.) \) \((a,a)\ \in \mathbb{N}\) \(2.) \) \((a,b)\ \in R \implies (b,a)\ \in R\) \(3.) \) \((a,b)\ \in R, (b,c)\ \in R\ \implies (a,c) \in R\)

  2. mathmath333
    • one year ago
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    @peachpi

  3. anonymous
    • one year ago
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    is (5,5) in R?

  4. mathmath333
    • one year ago
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    no

  5. anonymous
    • one year ago
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    suppose (5,25) is in R, is (25,5) in R?

  6. mathmath333
    • one year ago
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    no

  7. anonymous
    • one year ago
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    good. Try the last one

  8. anonymous
    • one year ago
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    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
    • one year ago
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    last one is false ?

  10. mathmath333
    • one year ago
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    yes it was written as \((a,a)\ \in \mathbb{N}\) for all \(a\ \in \mathbb{N}\) forgot to write that

  11. anonymous
    • one year ago
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    good. So the first two are definitely false.

  12. anonymous
    • one year ago
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    Typo. I meant to say if (25,5) is in R, then is (5,25) in R in part 2.

  13. mathmath333
    • one year ago
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    false

  14. anonymous
    • one year ago
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    ok. You said part c is false? Can you give a counterexample?

  15. mathmath333
    • one year ago
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    (1,1) , (1,1) -> (1,1)

  16. anonymous
    • one year ago
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    ok, but is true for ALL natural n?

  17. mathmath333
    • one year ago
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    no

  18. anonymous
    • one year ago
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    well. (256, 16) and (16, 4) are both in R, but (256,4) is not in R

  19. mathmath333
    • one year ago
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    so false

  20. anonymous
    • one year ago
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    yeah

  21. mathmath333
    • one year ago
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    ok thnx , it was easy i thought it was a way too hard

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