![]() ![]() For example, the statement "Tuesday is the day after Monday OR Thursday is the day after Saturday" would have a truth value of "true," because even though the latter statement is false, the former is true. OR: If two statements are joined together by "or," then the truth of the "or" statement is dependent upon whether one or both of the statements from which it is composed is true. However, the statement "Diamond is the hardest substance known to man AND diamonds are made of carbon" would be true, because both parts are true. While the former statement is true, the latter is not. For example, the statement "Diamond is the hardest substance known to man AND a diamond is a metal" is false. For example, the converse of the statement "If someone is a woman, then they are a human" would be "If someone is a human, then they are a woman." The converse of a conditional does not necessarily have the same truth value as the original, though it sometimes does, as will become apparent later.ĪND: And is a logical operator which is true only when both statements are true. A conditional is always in the form "If statement 1, then statement 2." In most mathematical notation, a conditional is often written in the form p ⇒ q, which is read as "If p, then q" where p and q are statements.Ĭonverse: the converse of a logical statement is when the conclusion becomes the condition and vice versa i.e., p ⇒ q becomes q ⇒ p. A conditional contains two parts: the condition and the conclusion, where the former implies the latter. Before one can start to understand logic, and thereby begin to prove geometric theorems, one must first know a few vocabulary words and symbols.Ĭonditional: a conditional is something which states that one statement implies another. ![]()
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