query: Prove that this set and operation comprise a group.
positive_passages.docid: 136300
positive_passages.text: {5,15,25,35} is a group under multiplication mod 40
negative_passages.docid: 114522
negative_passages.text: Prove that identity is unique in a group
negative_passages.docid: 132127
negative_passages.text: Proving a direct product of groups is a group
negative_passages.docid: 90590
negative_passages.text: Prove that the following set is dense
negative_passages.docid: 116707
negative_passages.text: Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
negative_passages.docid: 10602
negative_passages.text: Monotone Union of subgroups being subgroup
negative_passages.docid: 3543
negative_passages.text: Prove set is basis for $R^3$
negative_passages.docid: 111032
negative_passages.text: Proof of Sets involving the Cartesian Product
negative_passages.docid: 104308
negative_passages.text: Proving a set is a Sigma Algebra
negative_passages.docid: 2761
negative_passages.text: If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
negative_passages.docid: 122271
negative_passages.text: A subset of a transitive set is transitive
negative_passages.docid: 33233
negative_passages.text: Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
negative_passages.docid: 15210
negative_passages.text: Group of order 6 proof
negative_passages.docid: 117701
negative_passages.text: Let $G$ be a group and $X$ set. $a,b \in X$ are in the same orbit, so show that $stab(a) \cong stab (b)$
negative_passages.docid: 7416
negative_passages.text: Let $ A $, $ B $ and $ C $ be sets. If $ A \cup B = A \cup C $ and $ A \cap B = A \cap C $, then show that $ B = C $.
negative_passages.docid: 79452
negative_passages.text: How to prove that it is a group?
negative_passages.docid: 46240
negative_passages.text: Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.