Truth Table for dummies

Truth table is a mathematical table used in logic.

Truth table  means which the value of the predicates are true or False. If the values of predicates are always true then we can say that are tautologically implemented.

Ther are mainly four predicates available. They are

(1)AND (Conjuction)

(2)OR (Disjunction)

(3)Implication (Conditional)

(4)If and only if (Biconditional)

These Four type are very important to know the Truth values of the given table.

Prepositions Descriptions of Truth Tables for Dummies

AND (CONJUCTION):

If P and Q are two propositions then 'P and Q' are written as PΛQ is a proposition whose truth table value is TRUE only when both P and Q are TRUE.

OR (Disjunction):

If P and Q are two propostitions then 'P or Q' are written as PνQ is a proposition whose truth table values is FALSE only when both P and Q are FALSE.

IMPLICATION (CONDITIONAL):

If P and Q are any two propositions then 'P implies Q' are written as 'P->Q' is a proposition whose truth table values is FALSE only when P is TRUE and Q is FALSE.

IFF (BICONDITIONAL):

If P and Q are any two propositions then 'P IFF Q' writen as 'P<->Q' is truth table values is TRUE only when both P and Q have same truth value.

Negation:

If P is any Proposotion Then 'Not P' written as' ˜P ' is a proposition whose truth value is FALSE only when P is True.

Example:

If P = 2*3 = 5

Then ˜p = 2*3 ≠ 5

Note:

If the truth table of any proposition is true then we can say that it is Tautologically implemented.

Formulas:

PΛQ = P

PΛQ = Q

These both are simiplication formulas.

Proposition Logic with Truth Tables for Dummies

Proposition:

A declarative sentence to which we can assign.

True or False:

Every Truth table should contains the both true and false values.

Law of excluded Middle:

A proposition can not be simultaneously TRUE and FALSE.

Truth table for AND:

P Q PΛQ
T T T
T F F
F T F
F F F


Truth table for OR

P Q PνQ
T T T
T F T
F T T
F F F