List the members of sets

(i) \(B\)

(ii) \(C \cap B\)

(iii) \(B \cup C′\)

Consider the propositions:

p : x is a prime number less than 10.

q : x is a positive integer between 1 and 7.

Write down, in words, the contrapositive of the statement, “If x is a prime number less than 10, then x is a positive integer between 1 and 7.”

(i) \(B = 2, 3, 5, 7\)     (A1)

Brackets not required

(ii) \(C \cap B = 2, 3, 5\)     (A1)(ft)

Follow through only from incorrect B

(iii) \(C' = 0, 1, 7, 8, 9\)     (A1)(ft)

\(B \cup C' = 0, 1, 2, 3, 5, 7, 8, 9\)     (A1)(ft)

Note: Award (A1) for correct \(C'\) seen. The first (A1)(ft) in (iii) can be awarded only if C was listed incorrectly and a mark was lost as a result in (a)(ii). If C was not listed and \(C'\) is wrong, the first mark is lost. The second mark can (ft) within part (iii) as  well as from (i).     (C4)

[4 marks]

“If x is not a positive integer between 1 and 7, then x is not a prime number less than 10.”     (A1)(A1)

Award (A1) for both (not) statements, (A1) for correct order.     (C2)

[2 marks]

a) Many candidates included 1 as a prime number for set \(B\). Most candidates were able to list the intersection of \(B\) and \(C\) correctly with many receiving a follow through for their incorrect \(B\). Very few candidates were able to list \(B \cup C '\) correctly with many listing the intersection. It was disappointing that only a few candidates listed \(C'\) separately – those that did often received a mark for this working.

b) The majority of candidates were able to write down the contrapositive correctly but many gave the inverse or the converse instead.