Categories
Mathematics

Logic

LOGIC

A Proposition is a statement or sentence that either true or false but not both.  A simple statement or proposition is a statement containing no connectives.  In other words a proposition is considered simple.  If it cannot be broken up into sub-propositions.

On the other hand, a compound proposition is made up of two or more propositions joined by the connectives.  These connectives are and, or, if ….. Then, if and only if.  They are also called logic operators.

Logic operator symbol

And         ^

Or            ˅

If…..then \Rightarrow

If and only if      ⇔

not ~

THE TRUTH TABLES

The Truth or falsify of a proposition is its truth values.  A proposition that is true has a truth value T and a proposition that is false has a truth value of F.

CONJUCTIONDISJUNCTIONCONDITIONAL
P          q                    p ^ qP          q                   p v qP q                     p   \Rightarrow     q
T          T                       TT          T                   TT                        T         T
T          F                       FT          F                    TT                        F          F
F          T                       FF          T                    TF                        T          T
F          F                        FF          F                    F F                        F          T
P ^ Q is true when both p and q are trueP v q is false when both p and q are falseP     \Rightarrow     is false when p is T & q is F
BICONDITIONALNEGATION
P                       q                     p  ⇔   q P
T                       T                           TT                                   F
F                       T                           FF                                   T
F                       F                           T~
P ⇔ q is true when both p and q are either both true and both false. 

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