query: Define the binary operation $\bigtriangleup$ on $P(A)$ by $X \triangle Y = (X-Y) \cup (Y-X)$.Prove $\langle P(A), \triangle\rangle$ is group.
positive_passages.docid: 12459
positive_passages.text: Associativity of symmetric difference of sets
negative_passages.docid: 95935
negative_passages.text: Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
negative_passages.docid: 134687
negative_passages.text: Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
negative_passages.docid: 133480
negative_passages.text: new addition and new multiplication x ⊕ y = x + y − 1, x ⊗ y = x + y − xy on set Z, prove the set Z equipped with these 2 new operation
negative_passages.docid: 75017
negative_passages.text: Definition of General Associativity for binary operations
negative_passages.docid: 79165
negative_passages.text: How to show that $P(A\cup B) = P(A) + P(B) - P(A\cap B)$
negative_passages.docid: 71187
negative_passages.text: How to prove $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle$,using $[\hat{x},\hat{p}]=i\hbar$?
negative_passages.docid: 155233
negative_passages.text: $A=\emptyset $ if and only if $B = A \bigtriangleup B$
negative_passages.docid: 151559
negative_passages.text: Please help: How to show that Aut(G) is a subgroup of Sym(G)
negative_passages.docid: 116707
negative_passages.text: Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
negative_passages.docid: 150738
negative_passages.text: Proof of $(A - B) - C = A - (B \cup C)$
negative_passages.docid: 84397
negative_passages.text: $x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$
negative_passages.docid: 67637
negative_passages.text: How come $\lambda(\mathbb{Q})= \inf\left\{\sum_{n \ge 1} \lambda([a_n,b_n)) : \mathbb{Q} \subset \bigcup_{n \ge 1} [a_n,b_n)\right\} = 0$?
negative_passages.docid: 140190
negative_passages.text: Binary operation $xy$, has identity, but not associativity. Is the inverse unique?
negative_passages.docid: 143735
negative_passages.text: Prove/Disprove: For any sets $X$ and $Y$, $\overline{X\cap Y} = \bar{X}\cup\bar{Y}$
negative_passages.docid: 7890
negative_passages.text: Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
negative_passages.docid: 77297
negative_passages.text: Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$