query: Homework - Prove that a given set is a group
positive_passages.docid: 17997
positive_passages.text: Right identity and Right inverse implies a group
negative_passages.docid: 76635
negative_passages.text: Proof through combinatorial argument
negative_passages.docid: 56650
negative_passages.text: Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
negative_passages.docid: 70394
negative_passages.text: Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
negative_passages.docid: 134120
negative_passages.text: Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
negative_passages.docid: 86263
negative_passages.text: How do we show there are the same number of elements in each of the sets?
negative_passages.docid: 62687
negative_passages.text: Proving Cardinality of Cosets in Abstract Algebra
negative_passages.docid: 46240
negative_passages.text: Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
negative_passages.docid: 48523
negative_passages.text: Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
negative_passages.docid: 116707
negative_passages.text: Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
negative_passages.docid: 28223
negative_passages.text: Prove/Disprove that if two sets have the same power set then they are the same set
negative_passages.docid: 141379
negative_passages.text: All groups where underlying set has at most 4 elements
negative_passages.docid: 98542
negative_passages.text: Prove that $H$ is a subgroup of an abelian group $G$
negative_passages.docid: 39100
negative_passages.text: Exercise from Serre's "Trees" - prove that a given group is trivial
negative_passages.docid: 10180
negative_passages.text: How to prove that this set is closed?
negative_passages.docid: 24181
negative_passages.text: Showing that $G$ is a group under an alternative operation.
negative_passages.docid: 13834
negative_passages.text: Show that G is a group, if G is finite, the operation is associative, and cancellation law holds