Stuck with Venn Diagrams + Set Theory

[FallenAngelX]

I have recently been introduced to these, and understand them on there own and what effect they have. Eg: Unions, Intersects and Subsets

How ever i have the following problem infront of me and im completely stumped, or how to even start it so any help would be much appreciated.


Which of the following are always true for sets A,B?
A Union B is a subset of A

[FONT=verdana, geneva, lucida, lucida grande, arial, helvetica, sans-serif]How am i meant to prove or disprove this?

Thanks for the help[/FONT]

 

[pka]

Which of the following are always true for sets A,B?
A Union B is a subset of A
How am i meant to prove or disprove this?

You disprove it by giving a counterexample.

Give two sets \(\displaystyle A\;\& \;B\) such that \(\displaystyle A\cup B\not\subset A~.\)

This is quite easy.

 

[HallsofIvy]

I have recently been introduced to these, and understand them on there own and what effect they have. Eg: Unions, Intersects and Subsets

How ever i have the following problem infront of me and im completely stumped, or how to even start it so any help would be much appreciated.


Which of the following are always true for sets A,B?
A Union B is a subset of A

Do you know what "A union B" means? If you draw two circles, representing set A and B, what represents their union?

How am i meant to prove or disprove this?

There are many ways to do this, depending upon what kind of proofs your teacher wants. Since you title this "Venn Diagrams" perhaps just showing the Venn diagram for this situation. More rigorously, to prove "X is a subset of Y", you start with "if a is a member of X" and use the definitions of X and Y to conclude "then a is a member of Y". That is, show that any member of X is also a member of Y.

Thanks for the help