Preface

If you do not see at first how to solve a problem, don’t give up, think about it some more; be sure you understand all the terminology used in the problem, play with some ideas. If no approach presents itself, let it be and think about it again later. Repeat this process for days on end. When you finally wake up in the middle of the night with an idea, you’ll know you are putting in the right amount of effort for this course.”

1 - Formal Logic

A statement (or proposition) is a sentence that is either true or false.

...A, B, and C, are used to represent statements and are called statement letters;

the symbol ^ is a logical connective representing and

The expression A ^ B is called the conjunction of A and B, and A and B are called the conjuncts of this expression

Another connective is the word or, denoted by the symbol V.

The expression A V B (read “A or B”) is called the disjunction of A and B, and A and B are called the disjuncts of this expression

The logical connective here is implication, and it conveys the meaning that the truth of A implies or leads to the truth of B. In the implication A -> B, A stands for the antecedent statement and B stands for the consequent statement.

By convention, A -> B is considered true if A is false, regardless of the truth value of B.

Implication: Either both are true (like an if statement) or if the antecedent is false the result is true.

The equivalence connective is symbolized by <->.

(It's a shortcut) The expression A <-> B stands for (A -> B) ^ (B -> A).

The connectives we’ve seen so far are called binary connectives because they join two expressions together to produce a third expression.

a unary connective, a connective acting on one expression to produce a second expression

Negation is a unary connective.

The negation of A—­symbolized by A′—is read “not A.”

“If there is smoke, then there is fire.”

• If there is smoke (T) then there is fire (T) -> true
• If there is smoke (T) then there is fire (F) -> false
• If there is smoke (F) then there is fire (T) -> true
• If there is smoke (F) then there is fire (F) -> true

This order of precedence is

1. connectives within parentheses, innermost parentheses first
2. '
3. V ^
4. ->
5. <->