Logic Exam Ii

Front 1

Truth-Functional Statement

Back 1

Consists of two distinct simple statements, which are connected by and (a logical operator) and each simple statement has a truth value ( is either true or false)

Front 2

Logical Operator

Back 2

Words like "and" "not" "or" "if...then"

Front 3

Dot ( . )

Back 3

Means "and" and it's logical function is that it's a conjuction.

Ex: Q . P

if the . means that both P and Q need to be true for the whole thing thing to be TRUE

Front 4

Tilde (~)

Back 4

Not - it automatically negates the truth value of the phrase. to negate the truth value of a complex sentence just put the not in front of the complex statement.

Ex: It is NOT the case that...

Front 5

Wedge (v)

Back 5

Stands for "or"

or statements can be either inclusive (one part doesnt count on the other - meaning both can be true), or it can be exclusive (meaning both can't be true)

For P v Q it is only false when both are false.

Front 6

Conjunction ( . )

Back 6

and, but, while, however, also, moreover, although, yet, whereas

Front 7

Negation (~)

Back 7

not, it is not the case that, it is false that, it is not true that

Front 8

Disjunction (v)

Back 8

or, either....or, unless, otherwise

Front 9

Conditional (Horseshoe)

Back 9

P, then Q

The part that comes after "if" is called the antecendent and the part that follows the "then" is that consequent.

The ONLY time a conditional statement is false is when P is true and Q is false. it is true all other times.

Every time P then Q
Each time p then Q
All cases where P, then Q
In the event of P, then Q
On condition that P, then Q
Given that P, then Q
Provided that p, then Q
In any case where P, then Q
Supposing that P, Then Q
On any occurence that P, then Q
For every instance of P, then Q

Front 10

If and only if

Back 10

Whatever follows IF is the antecendent (P)

Whatever follows ONLY IF is the consequent (Q)

Front 11

Main logical operator

Back 11

the logical statement that determines the final truth value of the statement. Parentheses are an example.

Front 12

Contingent Statments

Back 12

statements that could be possibly true or possibly false

Front 13

Logically equivalent statements

Back 13

when two truth functional statements appear to be different but have the same truth table

Front 14

Contradictory Statements

Back 14

two statements that have opposite truth values on every line of their respective truth tables

Front 15

Consistent/inconsistent statements

Back 15

Consistent: there is at lease one line on their respective truth tables where both are true

Inconsistent: there is not even one line on their respective truth tables where both are true