Copy and complete the Venn diagram on your answer paper.

Write down the number of students who study Mathematics but not Further Mathematics.

Write down the total number of students in the school.

Write down \(n({\text{B}} \cup {\text{C}})\).

Write the following compound statement in symbolic form.

“It is snowing and the roads are not open.”

Write the following compound statement in words.

\((\neg p \wedge q) \Rightarrow r\)

An incomplete truth table for the compound proposition \((\neg p \wedge q) \Rightarrow r\) is given below.

Copy and complete the truth table on your answer paper.

     (A1)(A1)(A1)

Note: Award (A1) for each correct number in the correct position.

[3 marks]

28     (A1)(ft)

Note: 20 + their 8.

[1 mark]

59     (A1)(ft)

[1 mark]

10 + 12 + 20 + 6     (M1)

Note: Award (M1) for use of the correct regions.

= 48     (A1)(ft)(G2)

OR

59 − 8 − 3     (M1)

= 48     (A1)(ft)

[2 marks]

\(p \wedge \neg q\)     (A1)(A1)

Note: Award (A1) for \(\wedge\), (A1) for both statements in the correct order.

[2 marks]

If it is not snowing and the roads are open (then) we will go skiing.     (A1)(A1)(A1)

Note: Award (A1) for “if…(then)”, (A1) for “not snowing and the roads are open”, (A1) for “we will go skiing”.

[3 marks]

     (A1)(A1)(ft)(A1)(ft)

Note: Award (A1) for each correct column.

[3 marks]

This part was successfully attempted by the great majority. The less familiar form of the Venn diagram seemed not to cause too many problems, although a common mistake was the failure to add the 20 in set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not able to attempt this part.

This part was successfully attempted by the great majority. The less familiar form of the Venn diagram seemed not to cause too many problems, although a common mistake was the failure to add the 20 in set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not able to attempt this part.

This part was successfully attempted by the great majority. The less familiar form of the Venn diagram seemed not to cause too many problems, although a common mistake was the failure to add the 20 in set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not able to attempt this part.

This part was successfully attempted by the great majority. The less familiar form of the Venn diagram seemed not to cause too many problems, although a common mistake was the failure to add the 20 in set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not able to attempt this part.

The work on logic also proved accessible to the great majority with a large number of candidates attaining full marks. The most common errors were the omission of the “If” in the conditional statement in (b) and the inability to follow the implication in the truth table in (c).

The work on logic also proved accessible to the great majority with a large number of candidates attaining full marks. The most common errors were the omission of the “If” in the conditional statement in (b) and the inability to follow the implication in the truth table in (c).

The work on logic also proved accessible to the great majority with a large number of candidates attaining full marks. The most common errors were the omission of the “If” in the conditional statement in (b) and the inability to follow the implication in the truth table in (c).