DP Further Mathematics HL Questionbank

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Directly related questions

• 18M.2.hl.TZ0.6f: Find two elements in the same equivalence class which are inverses of each other with respect to...
• 18M.2.hl.TZ0.6e: Determine the equivalence classes into which R partitions S, giving the first four elements of...
• 16M.1.hl.TZ0.9b: The relation $R$ is defined on ${\mathbb{Z}^ + }$ by $nRm$ if and only if...
• 11M.1.hl.TZ0.3b: For $a,b \in \mathbb{Z}$ the relation $aRb$ is defined if and only if $\frac{a}{b} = {2^k}$...
• 10M.1.hl.TZ0.2a: Show that $R$ is an equivalence relation.
• 10M.1.hl.TZ0.2b: The relationship between $a$ , $b$ , $c$ and $d$ is changed to $ad - bc = n$ . State,...
• 09M.1.hl.TZ0.1a: Show that $R$ is an equivalence relation.
• 09M.1.hl.TZ0.1b: State the equivalence classes of $R$ .
• 13M.2.hl.TZ0.5c: Determine (i)     the equivalence class $E$ containing $1 + \sqrt 2$ ; (ii)     the...
• 13M.2.hl.TZ0.5d: Show that (i)     ${(1 + \sqrt 2 )^3} \in F$ ; (ii)     ${(1 + \sqrt 2 )^6} \in E$ .
• 13M.2.hl.TZ0.5a: Show that $R$ is an equivalence relation.
• 13M.2.hl.TZ0.5b: Show, by giving a counter-example, that the statement ${r_1}R{r_2} \Rightarrow r_1^2Rr_2^2$ is...
• 08M.2.hl.TZ0.4A.a: The relation ${R_1}$ is defined for $a,b \in {\mathbb{Z}^ + }$ by $a{R_1}b$ if and only if...
• 08M.2.hl.TZ0.4B.b: The relation ${R_2}$ is defined for $a,b \in {\mathbb{Z}^ + }$ by $a{R_2}b$ if and only if...
• 07M.2.hl.TZ0.5a: The relation $R$ is defined for $x,y \in {\mathbb{Z}^ + }$ such that $xRy$ if and only if...
• 14M.1.hl.TZ0.8: The group $\{ G,{\text{ }} * \}$ has a subgroup $\{ H,{\text{ }} * \}$. The relation $R$...
• 15M.1.hl.TZ0.15a: For ${\rho _1}$ and ${\rho _2}$ determine whether or not each is reflexive, symmetric and...
• 15M.1.hl.TZ0.15b: For each of ${\rho _1}$ and ${\rho _2}$ which is an equivalence relation, describe the...
• 15M.2.hl.TZ0.7b: A relation $R$ is defined on $S$ such that $A$ is related to $B$ if and only if there...