Copyright © University of Cambridge. All rights reserved.

## 'Twisty Logic' printed from http://nrich.maths.org/

### Why do this problem?

Logical paradoxes are an enduringly fascinating way to explore the
limits of logical thinking, and their consideration provides a
valuable mathematical workout. Students might be surprised to learn
that it is possible so simply to create logical statements with no
resolution True or False.

### Possible approach

These problems make an excellent poster display or end of lesson
filler; their intellectual challenge is appropriate at any stage of
study. However, they could also be used particularly productively
as a prequel to the study of logical operators in decision
mathematics.

Give the questions to the students and ask them to think about two
or three of them. Then ask the class to decide which ones are true
and which ones are false.Whilst many might intuitively 'get it'
that the statements are both true and false, explaining this
clearly presents a different challenge. Get the class clearly to
explain their reasoning to each other in pairs. Then suggest that
those with particularly good explanations give their reasoning to
the class.

### Key questions

IF the statement were true, THEN what would be the
implication?

IF the statement were false, THEN what would be the
implication?

### Possible support

To engage in this problem, students need to be confident with the
logical concepts of IF (something) THEN (something else) and basic
notions of True and False. Try the

circuit
maker problem from NRICH's

logic month to begin to explore these underlying issues.

### Possible extension

Could students make up similar questions of their own?

Could students change the questions slightly so that they are
either true or false?