Up: Elementary mathematical logic
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A sentence is made of simple propositions, which can be either true or false. These are called the truth values of a propsoition. We do not consider any possibility of maybe and the world is presented as black-an-white. For instance, a man is either tall or small, but not medium; he is cleaver or silly, but not ordinary. The contrary of rich is poor, and there is no middle class.
A sentence is made of elementary propositions, connected by the so-called logical connectors. The truth value is fixed by the truth values of the components, together with the rules to which the connectors obey.
When we intend to enounce the contrary of a complicated sentence, we have to find a sentence which includes all the possibilities which are not included in the original sentence, leaving no in-between situation.
We detail all this material in the following sections.