DP Mathematics HL Questionbank

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Directly related questions

• 18M.3srg.hl.TZ0.1a: Show that {T, ×10} is a group. (You may assume associativity.)
• 18M.3srg.hl.TZ0.1b: By making reference to the Cayley table, explain why T is Abelian.
• 16M.3srg.hl.TZ0.1b: Show that $\{ S,{\text{ }} * \}$ is an Abelian group.
• 17M.3srg.hl.TZ0.4a: Show that $\{ \mathbb{Z},{\text{ }} * \}$ is an Abelian group.
• 12M.3srg.hl.TZ0.1a: Associativity and commutativity are two of the five conditions for a set S with the binary...
• 12M.3srg.hl.TZ0.1b: The Cayley table for the binary operation $\odot$ defined on the set T = {p, q, r, s, t} is...
• 12N.3srg.hl.TZ0.3e: (i)     State the identity element for $\{ P(S){\text{, }}\Delta \}$. (ii)     Write down...
• 12N.3srg.hl.TZ0.3c: Prove that $\left\{ {P(A),{\text{ }}\Delta } \right\}$ is a group. You are allowed to assume...
• 12N.3srg.hl.TZ0.3f: Explain why $\{ P(S){\text{, }} \cup \}$ is not a group.
• 12N.3srg.hl.TZ0.3g: Explain why $\{ P(S){\text{, }} \cap \}$ is not a group.
• 12N.3srg.hl.TZ0.4h: Explain why $\{ G, * \}$ is an Abelian group.
• 08M.3srg.hl.TZ2.1: (a)     Draw the Cayley table for the set of integers G = {0, 1, 2, 3, 4, 5} under addition...
• 11M.3srg.hl.TZ0.1b: (i)     Show that {S , $*$} is a group. (ii)     Find the order of each element of {S ,...
• 10M.3srg.hl.TZ0.3: (a)     Consider the set A = {1, 3, 5, 7} under the binary operation $*$, where $*$...
• 13M.3srg.hl.TZ0.2c: Show that a new set G can be formed by removing one of the elements of S such that...
• 13M.3srg.hl.TZ0.2b: Give one reason why $\{ S,{\text{ }}{ \times _{14}}\}$ is not a group.
• 11N.3srg.hl.TZ0.1a: Consider the following Cayley table for the set G = {1, 3, 5, 7, 9, 11, 13, 15} under the...
• 11N.3srg.hl.TZ0.4b: The Cayley table for G is shown below.     The subgroup H is given as...
• 11N.3srg.hl.TZ0.1b: The Cayley table for the set...
• 14M.3srg.hl.TZ0.2a: (i)     Write down the six smallest non-negative elements of $S$. (ii)     Show that...
• 15N.3srg.hl.TZ0.4b: Prove that $\{ T,{\text{ }} * \}$ forms an Abelian group.
• 15M.3srg.hl.TZ0.5a: Show that $(G,{\text{ }} + )$ forms a group where $+$ denotes addition on $\mathbb{Q}$....