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Does 2 belongs to this set A? Does 2 an element of A..? (https://i.stack.imgur.com/Plc8B.jpg)

Shru
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  • Maybe tag as basic set theory. – coffeemath Apr 08 '18 at 21:55
  • It really annoys me that people downvote elementary maths questions, seemingly because they think "what is not obvious here?". But on another note, please rewrite the image using Latex. There's a reference here: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – it's a hire car baby Apr 14 '18 at 08:18
  • Furthermore, in respect of your question, here's the bit I think you missed: Sets can themselves be elements of sets, so in your image you have sets which are also elements or a larger set. So $2$ is not in itself an element of the set. $2\in{2}$ means $2$ is an element of ${2}$, and ${2}\in A$ but $2\notin A$ – it's a hire car baby Apr 14 '18 at 08:19

3 Answers3

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The answer to both questions is no.

$2$ is not an element of $A$ and { 2} is not an element of A either.

A has three elements, namely $1$, {2,3}, and {4} and none of the above is among them.

Mohammad Riazi-Kermani
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$A = \{1, \{2,3\}, \{4\}\}$

i) Is $2 \in A$. or Is $2$ an element of $A$?

Well.... What are the elements of $A$? The elements of $A$ are: a)$1$,b)$\{2,3\}$ and c) $\{4\}$. Are any of those three elements equal to $2$? No. None of them are equal to $2$. So $2 \not \in A$.

ii) Is $\{2\}\in A$. or Is $\{2\}$ an element of $A$?

Well.... What are the elements of $A$? The elements of $A$ are: a)$1$,b)$\{2,3\}$ and c) $\{4\}$. Are any of those three elements equal to $\{2\}$? No. None of them are equal to $\{2\}$. So $\{2\} \not \in A$.

fleablood
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Remove the outermost brackets. What's left is your elements, separted by commas. So here neither $2$ nor $\{2\}$ are elements.

coffeemath
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