Suppose that .
That means that . But that means .
What is wrong with that?
Hello,
I have been working on this proof for quite some time now can someone give me some pointers?
Prove: If A is a subset of B and B intersected with C= empty set then A intersected with C= empty set.
I know that if somehow I can prove that A intersected with B= empty set then I can use the laws of transitivity to come to prove my proof. I also know that if B intersected with C = empty set that means both B AND C are empty and contain no elements. If 'all the members' of A are in B and B= empty set then A= empty set as well.
Can someone help me piece this together please?
Prove: If A is a subset of B and B intersected with C= empty set then A intersected with C= empty set.
Okay so this is my proof attempt:
Suppose that A, B, and C are sets where A is a subset of B and B intersect C= empty set.
We know that empty set is the subset of each set. So, empty set is the subset A, empty set is the subset of B and empty set is the subset of C.
Since, empty set is the the subset of A and B then A intersect B is an empty set. If A intersect B= empty set and B intersect C equals empty set then A intersect C equals empty set (By laws of transitivity). **END OF PROOF**
P.S
Is the set A with a bar on top of it notation the same as the complement of A?
I GET THE GENERAL IDEA NOW!
Since A is the subset of B (A is IN B) and B intersect C have no elements in common (empty set, meaning they don't 'overlap'), then OF COURSE that A and C DONT have any elements in common as well (they also dont overlap because A is IN B).
Here it is:
Suppose that A, B, and C are sets where A is a subset of B and B intersect C= empty set.
Let x be an element of set A. If x E A and B intersect C= empty set, then x is NOT an element of C. Which means A is NOT a subset of C. Therefore, A intersect C= empty set as well (A and C cannot intersect and result in a NON-empty set if A is not a subset of C). If A intersect C= empty set and B intersect C= empty set, then A intersect C= EMPTY SET by laws of transitivity.
Can someone please help?! This is frustrating
How about now...
Suppose that A, B, and C are sets where A is a subset of B and B intersect C= empty set.
Let x be an element of set A. If x E A and B intersect C= empty set, then A is NOT a subset of C. Therefore, A intersect C= empty set as well (A and C cannot intersect and result in a NON-empty set if A is not a subset of C). If A intersect C= empty set and B intersect C= empty set, then A intersect C= EMPTY SET by laws of transitivity.
Cool down ,please read my posts again ,get out of your mind the transitivity law
When you solve a problem ,think before write or say anything.
Ask yourself what is given in a problem and what is asked to prove .
In a proof you must use all the given ,otherwise some where you must have gone wrong
My friend forgot to do that in a course final exam, but apparently he only proved a stronger result, so it's not always bad :POriginally Posted by xalk
On topic, matthayzon89 - take xalk's advice: Let , then and . Using the information you are given, what will you do next?