DP Mathematical Studies Questionbank

• Syllabus

3.4

Sub sections and their related questions

Converse, inverse, contrapositive.

• 10N.1.sl.TZ0.2c: Write down in words the contrapositive of the proposition given in part (b).
• 12N.1.sl.TZ0.9c: Write the converse of the following statement in symbolic form. “If Carlos is playing the guitar...
• 12M.1.sl.TZ1.6b: 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...
• 09N.1.sl.TZ0.7a: Write down the inverse of statement p in words.
• 09N.1.sl.TZ0.7b: Write down the converse of statement p in words.
• 09N.1.sl.TZ0.7c: Determine whether the converse of statement p is always true. Give an example to justify your...
• 13M.1.sl.TZ1.3b: Write down in words the inverse of the following compound proposition. If Yuiko is studying...
• SPM.1.sl.TZ0.10b: Write down in words, the inverse of the statement, \(s \Rightarrow q\) .
• 14M.1.sl.TZ2.2b: Write down, in words, the contrapositive statement of \(q \Rightarrow p\).
• 13N.1.sl.TZ0.3c: Write down, in symbolic form, the converse of \(\neg p \Rightarrow q\).
• 14M.1.sl.TZ1.14b: Write down in symbolic form the converse of the statement in (a).
• 14M.1.sl.TZ1.14d: Write down the name of the statement that is logically equivalent to the converse.
• 14N.1.sl.TZ0.5a: Write down in words, the inverse of \(p \Rightarrow q\).
• 14N.1.sl.TZ0.5b: Complete the following truth table.
• 14N.1.sl.TZ0.5c: State whether the converse and the inverse of an implication are logically equivalent. Justify...
• 15M.1.sl.TZ2.11c: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 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...

Logical equivalence.

• 09M.1.sl.TZ1.2d: The truth table for these compound propositions is given below. State the relationship between...
• 08M.1.sl.TZ2.1a: (i)     Complete the truth table below. (ii)    State whether the compound propositions...
• 14M.1.sl.TZ2.2c: Determine whether your statement in part (a) is logically equivalent to your statement in part...
• 14M.1.sl.TZ1.14c: Determine, without using a truth table, whether the statements in (a) and (b) are logically...
• 14M.1.sl.TZ1.14d: Write down the name of the statement that is logically equivalent to the converse.
• 14N.1.sl.TZ0.5c: State whether the converse and the inverse of an implication are logically equivalent. Justify...
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).

Testing the validity of simple arguments through the use of truth tables.

• 13M.1.sl.TZ1.6c: Using part (a), determine whether \(\neg p \vee q\) is true or false, for the case where \(x\) is...
• 13M.1.sl.TZ1.6d: Write down a value of \(x\) for which \(\neg p \vee q\) is false.
• SPM.1.sl.TZ0.3c: The argument \(\neg r \Rightarrow (q \vee p)\) is invalid. State the reason for this.
• SPM.1.sl.TZ0.10c: Determine the validity of the argument in (b). Give a reason for your decision.
• 14N.1.sl.TZ0.5c: State whether the converse and the inverse of an implication are logically equivalent. Justify...
• 15M.1.sl.TZ2.11d: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 15M.2.sl.TZ1.2c: Use your truth table to determine whether the argument in part (a) is valid. Give a reason for...
• 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...