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Date May 2010 Marks available 3 Reference code 10M.1.sl.TZ2.2
Level SL only Paper 1 Time zone TZ2
Command term Complete Question number 2 Adapted from N/A

Question

Complete the truth table shown below.

[3]
a.

State whether the compound proposition \((p \vee (p \wedge q)) \Rightarrow p\) is a contradiction, a tautology or neither.

 

[1]
b.

Consider the following propositions.

     p: Feng finishes his homework

     q: Feng goes to the football match

Write in symbolic form the following proposition.

If Feng does not go to the football match then Feng finishes his homework.

[2]
c.

Markscheme

     (A1)(A1)(ft)(A1)(ft)      (C3)

 

Note: Award (A1) for each correct column.

 

[3 marks]

a.

tautology     (A1)(ft)     (C1)

 

Note: Follow through from their last column.

 

[1 mark]

b.

\(\neg q \Rightarrow p\)     (A1)(A1)     (C2)


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

 

[2 marks]

c.

Examiners report

The truth table was very well answered and where the table was incorrect a follow through mark could be given for part (b) for a correct answer resulting from their final column. Some candidates appeared unsure of the concept of a tautology.

a.

The truth table was very well answered and where the table was incorrect a follow through mark could be given for part (b) for a correct answer resulting from their final column. Some candidates appeared unsure of the concept of a tautology.

b.

Nearly all candidates could write the proposition in part (c) in symbolic form.

c.

Syllabus sections

Topic 3 - Logic, sets and probability » 3.3 » Truth tables: concepts of logical contradiction and tautology.
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