thx Is the theorem correct? Justify your answer with either a proof on a counter
ID: 2961452 • Letter: T
Question
thx
Is the theorem correct? Justify your answer with either a proof on a counterexample. Prove that Prove that Suppose B is a set and F is a family of sets. Prove that Suppose F and G are nonempty families of sets and every element of F is disjoint from some element of G. Prove that and are disjoint. Prove that for any set A, Suppose F and G are families of sets. Prove that . What's wrong with the following proof that Proof Suppose This means that and . Thus, we can choose set A such that and Since . ThereforeExplanation / Answer
Power set of A is the set of all the subsets of A.
So it says that A is the union of all its subsets.
How do you prove it? When proving that two sets are equal, A = B, the standard argument is to show that A is a subset of B. Let x be an element of A. Then (some argument) it follows x is an element of B. Therefore x in A => x in B which means A is a subset of B. That's the definition of subset in terms of elements.
Then you do the same thing the other way. Let x be an element of B. Show x in B => x in A. Therefore B is a subset of A.
Since A subset B and B subset A, then A = B.
How does that work here?
1. Let x be an element of A. Argue that x in U(subsets of A), that is, that x is in at least one subset of A.
2. Let x be an element of U(subsets of A). That is x is in some subset of A. Show that means x is in A.
Both of those arguments are almost one-liners.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.