16. Only one of the following statements is true. Which one?
A 'B is true'
$B$ ' $E$ is false'
C 'Statements A to E are true'
D 'Statements A to E are false'
$E$ 'A is false'
Solution
E For statement A to be true, B would also have to be true. But we are told that only one statement is true, so this is not possible. We deduce that statement $\mathrm{A}$ is false. Therefore statement $\mathrm{E}$ is true.
In the context of the JMC you could stop here, because we have found one statement that must be true. However, we really ought to satisfy ourselves that statement E is the only one that is true.
As statement E is true, statement B is false. Statement D can never be true, because if statement $\mathrm{D}$ were true, all the statements, including $\mathrm{D}$, would be false, and we would have a contradiction. Because statement D must be false, statement $\mathrm{C}$ cannot be true.
So statement $\mathrm{E}$ is true and all the other statements are false.