DP Mathematics HL Questionbank
8.1
Description
[N/A]Directly related questions
- 18M.3srg.hl.TZ0.2b: Let S be a set containing \(n\) elements where \(n \in \mathbb{N}\). Show that S has \({2^n}\)...
- 18M.3srg.hl.TZ0.2a.ii: Verify that A \ C ≠ C \ A.
- 18M.3srg.hl.TZ0.2a.i: Find \(\left( {A \cup B} \right) \cap \left( {A \cup C} \right)\).
- 17N.3srg.hl.TZ0.2b.ii: In the context of the distributive law, describe what the result in part (b)(i) illustrates.
- 17N.3srg.hl.TZ0.2b.i: For sets \(P\), \(Q\) and \(R\), verify that \(P \cup (Q\Delta R) \ne (P \cup Q)\Delta (P \cup R)\).
- 17N.3srg.hl.TZ0.2a.ii: Represent the following set on a Venn diagram, \(A \cap (B \cup C)\).
- 17N.3srg.hl.TZ0.2a.i: Represent the following set on a Venn diagram, \(A\Delta B\), the symmetric difference of the...
- 17M.3srg.hl.TZ0.1b.ii: Hence by considering \(A \cap (B \cup C)\), verify that in this case the operation \( \cap \) is...
- 17M.3srg.hl.TZ0.1b.i: Write down all the elements of \(A \cap B,{\text{ }}A \cap C\) and \(B \cup C\).
- 17M.3srg.hl.TZ0.1a.ii: Determine the symmetric difference, \(A\Delta B\), of the sets \(A\) and \(B\).
- 17M.3srg.hl.TZ0.1a.i: Write down all the elements of \(A\) and all the elements of \(B\).
- 15N.3srg.hl.TZ0.1: Given the sets \(A\) and \(B\), use the properties of sets to prove that...
- 12M.3srg.hl.TZ0.2a: Given that \(R = (P \cap Q')'\) , list the elements of R .
- 12M.3srg.hl.TZ0.2b: For a set S , let \({S^ * }\) denote the set of all subsets of S , (i) find \({P^ *...
- 12N.3srg.hl.TZ0.3a: Write down all four subsets of A .
- 08M.3srg.hl.TZ2.3: Prove that \((A \cap B)\backslash (A \cap C) = A \cap (B\backslash C)\) where A, B and C are...
- 08N.3srg.hl.TZ0.1: \(A\), \(B\), \(C\) and \(D\) are subsets of \(\mathbb{Z}\)...
- 11M.3srg.hl.TZ0.2a: A \ B ;
- 11M.3srg.hl.TZ0.2b: \(A\Delta B\) .
- 09M.3srg.hl.TZ0.5: Prove that set difference is not associative.
- 11N.3srg.hl.TZ0.2a: Determine, using Venn diagrams, whether the following statements are true. (i) ...
- 11N.3srg.hl.TZ0.2b: Prove, without using a Venn diagram, that \(A\backslash B\) and \(B\backslash A\) are disjoint sets.
- 14M.3srg.hl.TZ0.3a: (i) Sketch the set \(X \times Y\) in the Cartesian plane. (ii) Sketch the set...
- 13N.3srg.hl.TZ0.5: (a) Given a set \(U\), and two of its subsets \(A\) and \(B\), prove...
- 14N.3srg.hl.TZ0.3c: Let \(P = \) {all permutations in \(A\) where exactly two integers change position}, and...
Sub sections and their related questions
Finite and infinite sets. Subsets.
- 12M.3srg.hl.TZ0.2a: Given that \(R = (P \cap Q')'\) , list the elements of R .
- 12M.3srg.hl.TZ0.2b: For a set S , let \({S^ * }\) denote the set of all subsets of S , (i) find \({P^ *...
- 12N.3srg.hl.TZ0.3a: Write down all four subsets of A .
- 11M.3srg.hl.TZ0.2a: A \ B ;
- 11M.3srg.hl.TZ0.2b: \(A\Delta B\) .
- 11N.3srg.hl.TZ0.2a: Determine, using Venn diagrams, whether the following statements are true. (i) ...
- 11N.3srg.hl.TZ0.2b: Prove, without using a Venn diagram, that \(A\backslash B\) and \(B\backslash A\) are disjoint sets.
- 14M.3srg.hl.TZ0.3a: (i) Sketch the set \(X \times Y\) in the Cartesian plane. (ii) Sketch the set...
- 13N.3srg.hl.TZ0.5: (a) Given a set \(U\), and two of its subsets \(A\) and \(B\), prove...
- 17N.3srg.hl.TZ0.2a.i: Represent the following set on a Venn diagram, \(A\Delta B\), the symmetric difference of the...
- 17N.3srg.hl.TZ0.2a.ii: Represent the following set on a Venn diagram, \(A \cap (B \cup C)\).
- 17N.3srg.hl.TZ0.2b.i: For sets \(P\), \(Q\) and \(R\), verify that \(P \cup (Q\Delta R) \ne (P \cup Q)\Delta (P \cup R)\).
- 17N.3srg.hl.TZ0.2b.ii: In the context of the distributive law, describe what the result in part (b)(i) illustrates.
- 18M.3srg.hl.TZ0.2a.i: Find \(\left( {A \cup B} \right) \cap \left( {A \cup C} \right)\).
- 18M.3srg.hl.TZ0.2a.ii: Verify that A \ C ≠ C \ A.
- 18M.3srg.hl.TZ0.2b: Let S be a set containing \(n\) elements where \(n \in \mathbb{N}\). Show that S has \({2^n}\)...
Operations on sets: union; intersection; complement; set difference; symmetric difference.
- 08M.3srg.hl.TZ2.3: Prove that \((A \cap B)\backslash (A \cap C) = A \cap (B\backslash C)\) where A, B and C are...
- 08N.3srg.hl.TZ0.1: \(A\), \(B\), \(C\) and \(D\) are subsets of \(\mathbb{Z}\)...
- 09M.3srg.hl.TZ0.5: Prove that set difference is not associative.
- 14N.3srg.hl.TZ0.3c: Let \(P = \) {all permutations in \(A\) where exactly two integers change position}, and...
- 15N.3srg.hl.TZ0.1: Given the sets \(A\) and \(B\), use the properties of sets to prove that...
- 18M.3srg.hl.TZ0.2a.i: Find \(\left( {A \cup B} \right) \cap \left( {A \cup C} \right)\).
- 18M.3srg.hl.TZ0.2a.ii: Verify that A \ C ≠ C \ A.
- 18M.3srg.hl.TZ0.2b: Let S be a set containing \(n\) elements where \(n \in \mathbb{N}\). Show that S has \({2^n}\)...
De Morgan’s laws: distributive, associative and commutative laws (for union and intersection).
- 15N.3srg.hl.TZ0.1: Given the sets \(A\) and \(B\), use the properties of sets to prove that...
- 18M.3srg.hl.TZ0.2a.i: Find \(\left( {A \cup B} \right) \cap \left( {A \cup C} \right)\).
- 18M.3srg.hl.TZ0.2a.ii: Verify that A \ C ≠ C \ A.
- 18M.3srg.hl.TZ0.2b: Let S be a set containing \(n\) elements where \(n \in \mathbb{N}\). Show that S has \({2^n}\)...
