MATH 123 Chapter Notes - Chapter 6: Mathematical Logic, Logical Biconditional, Contraposition
10 Aug 2017
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Symbolic logic uses letters to represent statements, and symbols for words such as: Not (negation, denoted by ~); if then (conditional, denoted by ); if and only if (biconditional, denoted by ). Statements are declarative sentences that are either true or false, but not both simultaneously. With logical connectives, multiple statements can be combined to form a compound statement. Truth tables explore truth values of various compound statements. We saw that two logical statements are equivalent (denoted ) if they have same truth value. Symbolic logic can design circuits and logical equivalences can simplify the circuits. The contrapositive, a statement related to the conditional, is equivalent to the original conditional statement, but two other related statements are not equivalent to the original conditional statement. These related statements are: the inverse, the converse. The contrapositive is equivalent to the original statement. However, the converse and inverse are not equivalent to the original statement, although they are equivalent to each other.
