query: Algebraic proof that collection of all subsets of a set (power set) of $N$ elements has $2^N$ elements
positive_passages.docid: 23557
positive_passages.text: Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
negative_passages.docid: 20973
negative_passages.text: How can I find all the subsets of a set, with exactly n elements?
negative_passages.docid: 74730
negative_passages.text: Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
negative_passages.docid: 87830
negative_passages.text: Relating the union of the power set of a set to the set itself
negative_passages.docid: 156006
negative_passages.text: Cardinality of set containing all infinite subsets of $\mathbb{Q}$
negative_passages.docid: 114262
negative_passages.text: Find the cardinality of the following set $S_n=\{(x,y)|x^2+y^2=n, \text{where }x,y,n \in \mathbb Z\text{ and }n\geq0 \}$
negative_passages.docid: 131983
negative_passages.text: Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
negative_passages.docid: 104274
negative_passages.text: Express $C$ interms of the sets $A_n$
negative_passages.docid: 88628
negative_passages.text: Proving the total number of subsets of S is equal to $2^n$
negative_passages.docid: 92534
negative_passages.text: Prove that any finite subset of a linearly independent set is linearly independent
negative_passages.docid: 5118
negative_passages.text: Show that $n ≤ 100$ if $ \{A_1,A_2,... ,A_n\}$ is a set of distinct $3$-element subsets of $\{1, 2,... , 36\}$ such that...
negative_passages.docid: 71133
negative_passages.text: prove inequlity about cardinality power sets
negative_passages.docid: 37331
negative_passages.text: Prove that every set with more than one element has a permutation without fixed points
negative_passages.docid: 100726
negative_passages.text: Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
negative_passages.docid: 148413
negative_passages.text: Proving $S_n$ is generated by the set $\{(1\text{ }2),(2\text{ }3),\cdots,(n-1\text{ }n)\}$ of $n-1$ transpositions.
negative_passages.docid: 21663
negative_passages.text: Bijection between power sets of sets implies bijection between sets?
negative_passages.docid: 140440
negative_passages.text: Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$