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 $A \subseteq B$, then you don't need the inner brackets inside set $B$. You can just say $B = \{-1, 0, 1, 2, 3\}$.

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

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

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

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

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