Logic is a mathematical tool that provides the user with an ability to distinguish whether a statement is true or false according to necessary rules. ### Logical Connectives What do these sentences have in common? - "If there is life on other planets, then aliens exist." - "A being is sentient if it has a sense of self and stream of inner experience." - "An action is ethical if and only if it produces the most possible good." All of these sentences rely on logical connectives to express the conditions which would make them true or false. #### Conjunction Conjunction is just a fancy conceptual name for the simple "and". When $A$ and $B$ are true, the sentence "$A$ and $Bquot; is true. If $A$ is not true, then $A$ and $B$ is not true. #### Disjunction Disjunction is the conceptual name for "or". Or means that only one thing needs to be true in order for the expression to be true. So if $A$ is true and $B$ is false, $A$ or $B$ is still true. However, if $A$ is false and $B$ is false, then $A$ or $B$ is false. #### Negation Negation means that the opposite of something is true. If $A$ is true, then *not* $A$ is false. And likewise, if $A$ is false, then *not* $A$ is true. #### Implication #### Equivalence ### Truth Tables ### Logical Equivalences