When I tell people that I am a mathematician it is often not very long before they bring up the subject of how logical mathematics is. Sometimes they consider this a downside to the subject as it makes it so much harder. After all, with logic you have to be right whereas in other areas of life opinions matter more. And it's easy to have an opinion – even if you can't back it up with evidence.

Logic is in essence quite simple despite its reputation for difficulty. A small number of simple rules exist. We need only to apply these and reduce complicated statements with them to achieve success.

In the next few chapters we shall concentrate on the logic used by mathematicians in their day-to-day work rather than on deep conundrums and paradoxes or on technical material such as predicates, compound statements and so on. I will, however, explain truth tables, which are rarely used by mathematicians in their everyday work, as they do provide a lot of clarity for beginners.

Mathematics is the business of proving mathematical statements to be true or false. So, first let's look at statements.