- #1
im2fastfouru
- 6
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This seems like a simple proof but I'm not familiar with power set proofs
If A[tex]\subseteq[/tex]B then P(A) [tex]\subseteq[/tex] P(B)
If A[tex]\subseteq[/tex]B then P(A) [tex]\subseteq[/tex] P(B)
im2fastfouru said:i'm more inclined to start with x [tex]\in[/tex] P(a), can i start the proof this way?
Why do you say "more inclined"? That was exactly what was suggested.im2fastfouru said:i'm more inclined to start with x [tex]\in[/tex] P(a), can i start the proof this way?
im2fastfouru said:i'm more inclined to start with x [tex]\in[/tex] P(a), can i start the proof this way?
what is x? In particular, what set are all of x's elements in?
im2fastfouru said:x is just an arbitrary element. And if A [tex]\subseteq[/tex] B then prove P(A) [tex]\subseteq[/tex] P(B). This need to be proved formally as well for my assignment!
A power set proof is a mathematical proof that demonstrates the number of subsets that a set has. It involves using the concept of power sets, which is the set of all possible subsets of a given set, including the empty set and the set itself.
A power set proof is important because it helps us understand the structure and size of a set. It also has applications in various fields of mathematics, such as set theory, combinatorics, and probability.
A power set proof is usually performed by using mathematical induction. This involves proving that the statement is true for the smallest possible set, usually the empty set, and then showing that if the statement is true for a set of size n, it is also true for a set of size n+1. This process is repeated until the statement is proven for all sets.
One common misconception about power set proofs is that they only apply to finite sets. In reality, power set proofs can also be used for infinite sets. Another misconception is that the power set of a set always has more elements than the original set, when in fact, they can have the same number of elements.
To improve your understanding of power set proofs, it is important to have a strong understanding of set theory and mathematical induction. Practice with different examples and try to break down the proof into smaller steps. You can also seek help from a teacher or tutor if you are struggling with the concept.