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Date May 2015 Marks available 2 Reference code 15M.1.sl.TZ2.11
Level SL only Paper 1 Time zone TZ2
Command term Determine Question number 11 Adapted from N/A

Question

     \(p:x\) is a multiple of \(12\)

     \(q:x\) is a multiple of \(6\).

Write down in words \(\neg p\).

[1]
a.

Write down in symbolic form the compound statement

\(r:\) If \(x\) is a multiple of \(12\), then \(x\) is a multiple of \(6\).

[2]
b.

Consider the compound statement

\(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple of \(12\).

Identify whether \(s:\) is the inverse, the converse or the contrapositive of \(r\).

[1]
c.

Consider the compound statement

\(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple of \(12\).

Determine the validity of \(s\). Justify your decision.

[2]
d.

Markscheme

\(x\) is not a multiple of \(12\)     (A1)     (C1)

a.

\(p \Rightarrow q\)     (A1)(A1)(C2)

Note: Award (A1) for \( \Rightarrow \), (A1) for \(p\) and \(q\) in the correct order.

Accept \(q \Leftarrow p\).

b.

Converse     (A1) (C1)

c.

not valid     (A1)

for example \(18\) is a multiple of \(6\) and not a multiple of \(12\)     (R1)     (C2)

 

Notes: Do not award (A1)(R0). Any multiple of 6 that is not a multiple of \(12\) can be accepted as a counterexample.

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 3 - Logic, sets and probability » 3.2 » Compound statements: implication, \( \Rightarrow \) ; equivalence, \( \Leftrightarrow \) ; negation, \(\neg \) ; conjunction, \( \wedge \) ; disjunction, \( \vee \) ; exclusive disjunction, \(\underline \vee \) .
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