DP Mathematical Studies Questionbank

• Syllabus

3.2

Sub sections and their related questions

Compound statements: implication, \( \Rightarrow \) ; equivalence, \( \Leftrightarrow \) ; negation, \(\neg \) ; conjunction, \( \wedge \) ; disjunction, \( \vee \) ; exclusive disjunction, \(\underline \vee \) .

• 10M.1.sl.TZ1.3b: Decide whether the compound...
• 11N.1.sl.TZ0.3b.i: State whether the statement \((p \wedge q) \Rightarrow (\neg p \underline \vee q)\) is a logical...
• 09M.1.sl.TZ1.2a: Write in words the compound proposition \(p \Rightarrow q\) ;
• 09M.1.sl.TZ1.2b: Write in words the compound proposition \(\neg p \vee q\).
• 07N.1.sl.TZ0.7c: Complete the following truth table.
• 09M.2.sl.TZ2.4ii, a: Write in words \((q \wedge \neg r) \Rightarrow \neg p\).
• 07M.1.sl.TZ0.4a: Explain the distinction between the compound propositions,...
• 07M.1.sl.TZ0.7b: Consider the propositions: p : x is a prime number less than 10. q : x is a positive integer...
• SPM.1.sl.TZ0.10a: Express in words the statement, \(s \Rightarrow q\) .
• 07N.1.sl.TZ0.7a: Write the sentence above using logic symbols.
• 07N.1.sl.TZ0.7b: Write in words \(s \Rightarrow \neg d\) .
• 08N.1.sl.TZ0.4a: Complete the truth table below for the symbolic statement \(\neg (p \vee q)\) .
• 08N.1.sl.TZ0.4b: Write down in words the meaning of the symbolic statement \(\neg (p \vee q)\).
• 08N.1.sl.TZ0.4c: Write in symbolic form the compound statement: “no food and no drinks may be taken into the...
• 08M.1.sl.TZ1.6a: Write in words, \(p \underline { \vee } q\).
• 08M.1.sl.TZ1.6b: Write in words, the converse of \(p \Rightarrow \neg q\).
• 08M.1.sl.TZ1.6c: Complete the following truth table for \(p \Rightarrow \neg q\).
• 08M.1.sl.TZ2.1b: Consider the following propositions. \(p:{\text{ Amy eats sweets}}\) ...
• 14N.1.sl.TZ0.5a: Write down in words, the inverse of \(p \Rightarrow q\).
• 15M.1.sl.TZ2.5a: Complete the following truth table.
• 15M.1.sl.TZ2.11b: Write down in symbolic form the compound statement \(r:\) If \(x\) is a multiple of \(12\), then...
• 15M.1.sl.TZ2.11c: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 15M.1.sl.TZ2.11d: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 15M.1.sl.TZ2.11a: Write down in words \(\neg p\).
• 15M.2.sl.TZ1.2a: Write the following argument in symbolic form. “If the land has been purchased and the building...
• 15M.2.sl.TZ1.2d: Write down the inverse of the argument in part (a) (i)     in symbolic form; (ii)     in words.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 17N.1.sl.TZ0.4a: Write down in words \((q \vee \neg r) \Rightarrow p\).
• 17N.1.sl.TZ0.4b: Complete the truth table.
• 17N.1.sl.TZ0.4c: State whether the statement \(\neg p \Rightarrow \neg (q \vee \neg r)\) is the inverse, the...
• 18M.1.sl.TZ2.2a: Write down, in words, \(\left( {q \wedge r} \right) \Rightarrow \neg p\).
• 18M.1.sl.TZ2.2b: Complete the following truth table.
• 18M.1.sl.TZ2.2c: State whether \(\left( {q \wedge r} \right) \Rightarrow \neg p\) is a tautology, contradiction or...

Translation between verbal statements and symbolic form.

• 10M.1.sl.TZ2.2c: Consider the following propositions.      p: Feng finishes his homework      q: Feng goes to...
• 10N.1.sl.TZ0.2b: Consider the propositions      p: Cristina understands logic      q: Cristina will do well on...
• 12N.1.sl.TZ0.9a: Write in words the compound statement \(\neg p \wedge q\) .
• 12N.1.sl.TZ0.9b: Write the following statement in symbolic form. “Either Carlos is playing the guitar or he is...
• 12N.1.sl.TZ0.9c: Write the converse of the following statement in symbolic form. “If Carlos is playing the guitar...
• 12M.1.sl.TZ1.6a: Write down, in words, the statement p \(\Rightarrow\) q.
• 12M.1.sl.TZ1.6b: Write down, in words, the inverse of the statement p \(\Rightarrow\) q.
• 12M.1.sl.TZ1.6c: State whether the inverse of the statement p \( \Rightarrow \) q is always true. Justify your...
• 12M.1.sl.TZ2.2b: Write the following compound proposition in symbolic form. “I cannot swim 50 metres and I take...
• 12M.1.sl.TZ2.2c: Write the following compound proposition in words. \(q \Rightarrow \neg q \)
• 09N.2.sl.TZ0.2B, a: Write the following compound statement in symbolic form. “It is snowing and the roads are not...
• 09N.2.sl.TZ0.2B, b: Write the following compound statement in words. \((\neg p \wedge q) \Rightarrow r\)
• 11M.1.sl.TZ1.4b: What Anna said was lost by the police, but in symbolic form it...
• 11M.1.sl.TZ1.4a: Write down Matthew’s statement in symbolic logic form.
• 09M.2.sl.TZ2.4ii, a: Write in words \((q \wedge \neg r) \Rightarrow \neg p\).
• 09M.2.sl.TZ2.4ii, b, i: Consider the statement “If the number is a multiple of five, and is not even then it will not end...
• 11M.1.sl.TZ2.3a: Write, in words, the compound proposition\[\neg h \Rightarrow (p \vee a)\].
• 13M.1.sl.TZ1.3a: Write down the following compound propositions in symbolic form. (i) Yuiko is studying French...
• 13M.1.sl.TZ1.6b: Consider the propositions p and q: p: x is a number less than 10. q: x2 is a number greater...
• 13M.1.sl.TZ2.2a: Write the following compound proposition in symbolic form. If students do not stay up late then...
• 07M.1.sl.TZ0.7b: Consider the propositions: p : x is a prime number less than 10. q : x is a positive integer...
• SPM.1.sl.TZ0.3a: Write the following argument in words\[\neg r \Rightarrow (q \vee p)\]
• SPM.1.sl.TZ0.10a: Express in words the statement, \(s \Rightarrow q\) .
• SPM.1.sl.TZ0.10b: Write down in words, the inverse of the statement, \(s \Rightarrow q\) .
• 07N.1.sl.TZ0.7a: Write the sentence above using logic symbols.
• 07N.1.sl.TZ0.7b: Write in words \(s \Rightarrow \neg d\) .
• 08N.1.sl.TZ0.4b: Write down in words the meaning of the symbolic statement \(\neg (p \vee q)\).
• 08N.1.sl.TZ0.4c: Write in symbolic form the compound statement: “no food and no drinks may be taken into the...
• 08M.1.sl.TZ1.6a: Write in words, \(p \underline { \vee } q\).
• 08M.1.sl.TZ1.6b: Write in words, the converse of \(p \Rightarrow \neg q\).
• 09M.2.sl.TZ2.4ii, b, ii: Consider the statement “If the number is a multiple of five, and is not even then it will not end...
• 14M.1.sl.TZ2.2a: Write down the following statement in words. \[q \Rightarrow p\]
• 14M.1.sl.TZ2.2b: Write down, in words, the contrapositive statement of \(q \Rightarrow p\).
• 13N.1.sl.TZ0.3a: Write down, in words, the compound proposition \(\neg p \Rightarrow q\).
• 14M.1.sl.TZ1.3a: Write the following compound proposition in words. \[(p \wedge q) \Rightarrow \neg r\]
• 14M.1.sl.TZ1.14a: Express the following in symbolic form. “A rectangle always has two diagonals that are equal in...
• 14N.1.sl.TZ0.5a: Write down in words, the inverse of \(p \Rightarrow q\).
• 15M.1.sl.TZ2.11b: Write down in symbolic form the compound statement \(r:\) If \(x\) is a multiple of \(12\), then...
• 15M.1.sl.TZ2.11c: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 15M.1.sl.TZ2.11a: Write down in words \(\neg p\).
• 15M.2.sl.TZ1.2a: Write the following argument in symbolic form. “If the land has been purchased and the building...
• 15M.2.sl.TZ1.2d: Write down the inverse of the argument in part (a) (i)     in symbolic form; (ii)     in words.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 17N.1.sl.TZ0.4a: Write down in words \((q \vee \neg r) \Rightarrow p\).
• 17N.1.sl.TZ0.4b: Complete the truth table.
• 17N.1.sl.TZ0.4c: State whether the statement \(\neg p \Rightarrow \neg (q \vee \neg r)\) is the inverse, the...
• 18M.1.sl.TZ2.2a: Write down, in words, \(\left( {q \wedge r} \right) \Rightarrow \neg p\).
• 18M.1.sl.TZ2.2b: Complete the following truth table.
• 18M.1.sl.TZ2.2c: State whether \(\left( {q \wedge r} \right) \Rightarrow \neg p\) is a tautology, contradiction or...