DP Further Mathematics HL Questionbank
Relations: equivalence relations; equivalence classes.
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[N/A]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...
