1.2Conditional and Biconditional Connectives
1.2.1 The Conditional Sentence
The conditional sentence (or implication), is a compound sentence of the form
“if P then Q”
From a purely logical point of view, conditional sentences do not necessarily imply a cause and effect between P and Q, although generally there is a definite cause and effect. For example the conditional sentence
If 1 + 1 = 3, then pigs fly.
is a true conditional sentence, although the reader would have to think long and hard to find a cause and effect relation between 1 + 1 = 3 and flying pigs. A more common implication in mathematics would be
If a positive integer n is composite, then n has a prime divisor less than or equal to
.
which provides an important cause and effect between P and Q. No doubt the reader has seen conditional sentences in Euclidean geometry, where the subject is explained through cause and effect implications of this type. The sentence, “If a polygon has three sides, then it is a triangle,” is a conditional sentence relating two important concepts in geometry.
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