Category Archives: Logic

Basic Logic Tables

Definitions:

\vee \quad Or\\ \\ \wedge \quad And\\ \\ \neg \quad Not\\ \\ \forall \quad For\quad All\\ \\ \exists \quad There\quad exists\\ \\ \Rightarrow \quad Implies

LOGICAL POSSIBILITIES:

TRUE (T) FALSE (F)
TRUE (T) T, T T, F
FALSE (F) F, T F, F

“OR” TRUTH TABLE:

a b a\vee b
T T T
T F T
F T T
F F F

“AND” TRUTH TABLE

a b a\wedge b
T T T
T F F
F T F
F F F

“NOT” TRUTH TABLE

a \neg a
T F
F T

“IMPLIES” TRUTH TABLE

a b a\Rightarrow b
T T T
T F F
F T T
F F T

More Mathematical Logic

Axioms of equality are basic rules for using the equals sign…

The Additive Axiom Of Equality:

If a=b and c=d, then a+c=b+d.

The Additive Axiom Of Inequality:

If a>b, then a+c>b+c.

Identity Element For Addition:

Any number added to 0 gives the original number, for instance, n+0=n.

Identity Element For Multiplication:

Any number multiplied by 1 gives the original number, for instance, n*1=n.

Multiplicative Axiom Of Equality:

If a=b and c=d, then ac=bd.

Negative Multiplication Property Of Inequality:

You must reverse the inequality sign when multiplying or dividing by a negative number.