Medisonmuta
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- Jan 28, 2016
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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
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....
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?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!
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?C= is a subset
So the dotted circle means the following?⊙ is an empty set
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 = ⊙ \(\displaystyle A\subseteq B\iff A\setminus B =\emptyset\)
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!
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?C= is a subset
. . . . .\(\displaystyle \mbox{a. }\, \subset\)
. . . . .\(\displaystyle \mbox{b. }\, \subseteq\)
So the dotted circle means the following?⊙ is an empty set
. . . . .\(\displaystyle \mbox{c. }\, \emptyset\)
Okay; great! Now:b and c is that what I mean
We're still waiting on this information. Thank you!What are your responses to my other questions? When you reply, please include a clear listing of your thoughts and efforts so far.
Okay; great! Now:
We're still waiting on this information. Thank you!
We've been able to obtain clarification from you regarding some of the questions posed. What remains is:You have already cleared above.
Until you've replied with definitions, there is no way to begin to assist.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?
Okay. But first, please reply and...Just help me how to prove it.
Once we can see what you're tried and where you're getting stuck, we can reply with helps and suggestions. Thank you!...please include a clear listing of your thoughts and efforts so far.