A truth table is a mathematical table, used in Boolean Algebra. In Boolean Algebra a proposition is an Assertion which is either True or False (but not both). A Truth Table depicts all possible combinations of the truth value ( T or F) of the propositional variables. Propositional variables are denoted by P, Q , R… etc. In case of two propositional variables there would be four possible combinations of truth values . In case of three propositional variables there would be eight possible combinations. This is shown in the two tables shown below. The first table shows the possible combinations of two propositional variables P and Q. The other table shows the possible combinations of three variables P,Q and R. T represents(True) F represents (False).
P Q
|
T |
T |
|
T |
F |
|
F |
T |
|
F |
F |
P Q R
|
T |
T |
T |
|
T |
T |
F |
|
T |
F |
T |
|
T |
F |
F |
|
F |
T |
T |
|
F |
T |
F |
|
F |
F |
T |
|
F |
F |
F |
These truth tables are used to examine the truth value of logical connectives. Some logical connectives are 1. P or Q, ( P v Q)
2.P and Q ( P^ Q)
3.not P. ( ~P )
4. Either
P or Q ( P
Q)
5. P implies Q (P→ Q)
6. P implies Q and Q implies P (P↔Q)
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