I need help with these questions

[Medisonmuta]

I have a problem especially proving the formulas in set theory.I just need help question no.1.51 to 1.55. Anyone know one of them

 

[Deleted member 4993]

I have a problem especially proving the formulas in set theory.I just need help question no.1.51 to 1.55. Anyone know one of them

too small an image to decipher....

 

[Ishuda]

I have a problem especially proving the formulas in set theory.I just need help question no.1.51 to 1.55. Anyone know one of them

In addition to Subhotosh Khan post, you should also note that this site expects the posters to show (or at least talk through) their own attempt at solving the problem. So, what are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

 

[Medisonmuta]

too small an image to decipher....

1.Prove the following

(a)A C= B if only if A n B'=⊙
(b)A C= B if only if A'u B=U
(c)A C= B if only if B' C= A'
(d)A C= B if only if A/B = ⊙

 

[stapel]

1.Prove the following

(a)A C= B if only if A n B'=⊙

Please define your terms. Are A, B, C, and U meant to be sets? What is meant by "A C"? Does "if only if" mean "if and only if"? Are you using "n" to mean "intersect" and "u" to mean "union"? Does the "prime" notation indicate set complementation? What is the meaning of the dotted circle at the end of the quoted line above?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

 

[Medisonmuta]

Please define your terms. Are A, B, C, and U meant to be sets? What is meant by "A C"? Does "if only if" mean "if and only if"? Are you using "n" to mean "intersect" and "u" to mean "union"? Does the "prime" notation indicate set complementation? What is the meaning of the dotted circle at the end of the quoted line above?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

C= is a subset
⊙ is an empty set

 

[stapel]

C= is a subset

Does "C=" mean "is a subset of", or does it mean "is a subset of, or is equal to"? In other words, which of the following do you mean?

. . . . .\(\displaystyle \mbox{a. }\, \subset\)

. . . . .\(\displaystyle \mbox{b. }\, \subseteq\)

⊙ is an empty set

So the dotted circle means the following?

. . . . .\(\displaystyle \mbox{c. }\, \emptyset\)

What are your responses to my other questions? When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

 

[pka]

1.Prove the following

(a)A C= B if only if A n B'=⊙ \(\displaystyle A\subseteq B\iff A\cap B' =\emptyset \)
(b)A C= B if only if A'u B=U \(\displaystyle [A\subseteq B\iff A'\cup B' =\mathcal{U}\)
(c)A C= B if only if B' C= A' \(\displaystyle A\subseteq B\iff B'\subseteq A' \)
(d)A C= B if only if A/B = ⊙ \(\displaystyle A\subseteq B\iff A\setminus B =\emptyset\)

........................\(\displaystyle \emptyset \)

 

[Medisonmuta]

Does "C=" mean "is a subset of", or does it mean "is a subset of, or is equal to"? In other words, which of the following do you mean?

. . . . .\(\displaystyle \mbox{a. }\, \subset\)

. . . . .\(\displaystyle \mbox{b. }\, \subseteq\)


So the dotted circle means the following?

. . . . .\(\displaystyle \mbox{c. }\, \emptyset\)

What are your responses to my other questions? When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

b and c is that what I mean

 

[stapel]

C= is a subset

Does "C=" mean "is a subset of", or does it mean "is a subset of, or is equal to"? In other words, which of the following do you mean?

. . . . .\(\displaystyle \mbox{a. }\, \subset\)

. . . . .\(\displaystyle \mbox{b. }\, \subseteq\)

⊙ is an empty set

So the dotted circle means the following?

. . . . .\(\displaystyle \mbox{c. }\, \emptyset\)

b and c is that what I mean

Okay; great! Now:

What are your responses to my other questions? When you reply, please include a clear listing of your thoughts and efforts so far.

We're still waiting on this information. Thank you!

 

[Medisonmuta]

Okay; great! Now:


We're still waiting on this information. Thank you!

You have already cleared above. Just help me how to prove it.

 

[stapel]

You have already cleared above.

We've been able to obtain clarification from you regarding some of the questions posed. What remains is:

Please define your terms.... Does "if only if" mean "if and only if"? Are you using "n" to mean "intersect" and "u" to mean "union"? Does the "prime" notation indicate set complementation? What is the meaning of the dotted circle at the end of the quoted line above?

Until you've replied with definitions, there is no way to begin to assist.

Just help me how to prove it.

Okay. But first, please reply and...

...please include a clear listing of your thoughts and efforts so far.

Once we can see what you're tried and where you're getting stuck, we can reply with helps and suggestions. Thank you!