Consider the following propositions:

\(p:\) The lesson is cancelled

\(q:\) The teacher is absent

\(r:\) The students are in the library.

Write, in words, the compound proposition \(q \Rightarrow (p \wedge r).\)

Complete the following truth table.

Hence, justify why \(q \Rightarrow \neg r\)  is not a tautology.

if the teacher is absent then the lesson is cancelled and the students are in the library        (A1)(A1)(A1)   (C3)

Note: Award (A1) for If…then.
For Spanish candidates, only accept “Si” and “entonces”.
For French candidates, only accept “Si” and “alors”.
For all three languages these words are from the subject guide.
Award (A1) for “and”,
Award (A1) for correct propositions in correct order.

(A1)(A1)(ft)   (C2)

Note: Award (A1) for \(\neg r\) column correct and (A1) for \(q \Rightarrow \neg r\) column correct.
Award (A0)(A1)(ft) for a \(q \Rightarrow \neg r\) column that correctly follows from an incorrect \(\neg r\) column.

not all of the entries are true (or equivalent)        (R1)    (C1)

Note: Accept “One entry is false”.

Question 4: Logic.
All candidates recognized that to fill in a truth table the answer is either true or false. However, given that there are truth tables in the formula booklet it was surprising that some candidates made mistakes when negating a given column of the truth table. Most candidates recognized that in a tautology the column is always true with a small minority confusing tautology and contradiction. Candidates were able to write a compound proposition in words.

Question 4: Logic.
All candidates recognized that to fill in a truth table the answer is either true or false. However, given that there are truth tables in the formula booklet it was surprising that some candidates made mistakes when negating a given column of the truth table. Most candidates recognized that in a tautology the column is always true with a small minority confusing tautology and contradiction. Candidates were able to write a compound proposition in words.

Question 4: Logic.
All candidates recognized that to fill in a truth table the answer is either true or false. However, given that there are truth tables in the formula booklet it was surprising that some candidates made mistakes when negating a given column of the truth table. Most candidates recognized that in a tautology the column is always true with a small minority confusing tautology and contradiction. Candidates were able to write a compound proposition in words.