Logical Form

•          Logical Form

–        Initial terms in logic: sentence, true, false

–        Statement (proposition) is a sentence that is true or false but not both

–        Compound statement is a statement built out of simple statements using logical operations: negation, conjunction, disjunction

–        Truth table

–        Precedence of logical operations

–        English words to logic:

•          It is not hot but it is sunny

•          It is neither hot nor sunny

–        Statement form (propositional form) is an expression made up of statement variables and logical connectives (operators)

–        Exclusive OR: XOR

–        Truth table for (~p Ù q) Ú (q Ù ~r)

–        Two statements are called logically equivalent if and only if (iff) they have identical truth tables

–        Double negation

–        Non-equivalence: ~(p Ú q) vs ~p Ú ~q

–        De Morgan’s Laws:

–        The negation of and AND statement is logically equivalent to the OR statement in which component is negated

–        The negation of an OR statement is logically equivalent to the AND statement in which each component is negated

–        Applying De-Morgan’s Laws:

•          Write negation for

•          The bus was late or Tom’s watch was slow

•          -1 < x <= 4

–        Tautology is a statement that is always true regardless of the truth values of the individual logical variables

–        Contradiction is a statement that is always false regardless of the truth values of the individual logical variables