DP Mathematics HL Questionbank

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Directly related questions

• 18M.3srg.hl.TZ0.4c: Let \(f{\text{:}}\,{S_4} \to {S_4}\) be defined by \(f\left( p \right) = p \circ p\)...
• 16M.3srg.hl.TZ0.3: The group \(\{ G,{\text{ }} * \} \) is Abelian and the bijection \(f:{\text{ }}G \to G\) is...
• SPNone.3srg.hl.TZ0.4: The groups \(\{ K,{\text{ }} * \} \) and \(\{ H,{\text{ }} \odot \} \) are defined by the...
• 14M.3srg.hl.TZ0.4b: (i)     Prove that the kernel of \(f,{\text{ }}K = {\text{Ker}}(f)\), is closed under the group...
• 14M.3srg.hl.TZ0.4a: Prove that \(f({e_G}) = {e_H}\), where \({e_G}\) is the identity element in \(G\) and \({e_H}\)...
• 15N.3srg.hl.TZ0.5a: Prove that the function \(f\) is a homomorphism from the group...
• 14N.3srg.hl.TZ0.4c: Given that \(f(x * y) = p\), find \(f(y)\).
• 14N.3srg.hl.TZ0.4a: Prove that for all \(a \in G,{\text{ }}f({a^{ - 1}}) = {\left( {f(a)} \right)^{ - 1}}\).
• 14N.3srg.hl.TZ0.4b: Let \(\{ H,{\text{ }} \circ \} \) be the cyclic group of order seven, and let \(p\) be a...