1. ## Sets

Here is the problem
Give examples of three sets

1.A (subset) B (proper subset) c
2. Ais in B, B is in C and A is not a part of C
3. Ais in B and A (propersubset) C

1. A= {0,1,2} B=(-1,{0,1,2}, 3} c= {-1,3}
2.A = {1} B= {{1},2,3} c= ?
3. A= {1,2,3} B= {0,1,2,3,4} C= {{1,2},4}

any help?are they right? wrong? where am i confused? any help thanks

2. Hello j5sawicki
Originally Posted by j5sawicki
Here is the problem
Give examples of three sets

1.A (subset) B (proper subset) c
2. Ais in B, B is in C and A is not a part of C
3. Ais in B and A (propersubset) C

1. A= {0,1,2} B=(-1,{0,1,2}, 3} c= {-1,3}
2.A = {1} B= {{1},2,3} c= ?
3. A= {1,2,3} B= {0,1,2,3,4} C= {{1,2},4}

any help?are they right? wrong? where am i confused? any help thanks
You haven't made the questions clear. What, for example, does 'A is not a part of C' mean?

However, #1 looks clear enough, and your answer is incorrect. If $\displaystyle A \subseteq B$, then you don't need the inner brackets inside set $\displaystyle B$. You can just say $\displaystyle B = \{-1, 0, 1, 2, 3\}$.

And if $\displaystyle B \subset C$, then $\displaystyle C$ needs to contain all the elements that are in $\displaystyle B$, plus at least one other. You have this the wrong way round; you have $\displaystyle C \subset B$.

For #2, I assume you mean $\displaystyle A \in B$ and $\displaystyle B\in C$, but I don't know (as I've said) what 'not a part of' means.

If $\displaystyle A \in B$, and $\displaystyle A$ is itself a set, then your first answer is correct: $\displaystyle A=\{1\}, B =\{\{1\},2,3\}$. But it would be better if you didn't mix sets with integers in set $\displaystyle B$. So $\displaystyle B = \{\{1\},\{2\},\{3\}\}$ would probably be a better answer.

If $\displaystyle B \in C$, then $\displaystyle C$ must be a set containing sets like $\displaystyle B$ as elements - and include $\displaystyle B$ itself. For instance you could have $\displaystyle C = \{\{\{1\},\{2\},\{3\}\}, \{\{1\},\{2\}\}\}$

For #3, you could have $\displaystyle A$ and $\displaystyle B$ the same as in #2, and then if $\displaystyle A\subset C,\, C$ must contain all the elements in $\displaystyle A$, plus at least one more; for example, $\displaystyle C = \{1, 2\}$