A Logical Connective (also called a logical operator) is a symbol or a word which is used to connect two or more sentences. Each logical connective can be expressed as a truth function.
In logical reasoning, we deal with statements that are essentially sentences in English language. However, factual correctness is not important. We are only interested in logical truthfulness of the statements. We can represent simple statements using symbols like p and q. When simple statements are combines using logical connectives, compound statements are formed.
Negation is the opposite of a statement. For example,
When two statements are connected using OR, at least one of them is true. For example,
In such situation, valid inference is If p did not happen, then q must happen. And If p did not happen, then p must happen.
When two statements are connected using AND, both statements have to be true for compound statement to be true.
If p, then q (p --> q): It is read as p implies q. It means that if we know p has occured, we can conclude that q has occured. In such situations, only valid inference is "If ~q, then ~p"; If q did not happen, then p did not happen.
Examine the following statements:
Which one of the following conclusions is valid in the context of the above statements?