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Date May 2014 Marks available 2 Reference code 14M.1.sl.TZ2.2
Level SL only Paper 1 Time zone TZ2
Command term Determine Question number 2 Adapted from N/A

Question

Two propositions \(p\) and \(q\) are defined as follows

     \(p\): Eva is on a diet

     \(q\): Eva is losing weight.

Write down the following statement in words.

\[q \Rightarrow p\]

[2]
a.

Write down, in words, the contrapositive statement of \(q \Rightarrow p\).

[2]
b.

Determine whether your statement in part (a) is logically equivalent to your statement in part (b). Justify your answer.

[2]
c.

Markscheme

If Eva is losing weight then Eva is on a diet     (A1)(A1)     (C2)

 

Notes: Award (A1) for If… then…

     For Spanish candidates, only accept “Si” and “entonces”.

     For French candidates, only accept “Si” and “alors”.

     For all 3 languages these words are from the subject guide.

     Award (A1) for correct propositions in correct order.

 

[2 marks]

a.

If Eva is not on a diet then she is not losing weight     (A1)(A1)     (C2)

 

Notes: Award (A1) for “not on a diet” and “not losing weight” seen, (A1) for complete correct answer.

     No follow through from part (a).

 

[2 marks]

b.

The statements are logically equivalent     (A1)(ft)

The contrapositive is always logically equivalent to the original statement     (R1)(ft)

OR

A correct truth table showing the equivalence     (R1)(ft)     (C2)

 

Note: Follow through from their answers to part (a) and part (b).

 

[2 marks]

c.

Examiners report

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

Syllabus sections

Topic 3 - Logic, sets and probability » 3.4 » Logical equivalence.

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