Truth table is a table showing the truth value of a statement formula for each possible combinations of truth values of component statements. A statement formula having n distinct components will have 2$^{2}$ rows in its truth table. A statement is a declarative sentence which has one and only one of the two possible values, called truth values. These two truth values are true and false denoted by the symbols T and F respectively, sometimes also denoted by symbols 1 and 0. Since we allow only two possible truth values, this logic is called two-valued logic.
Truth table is a powerful concepts that constructs truth tables for its component statements. It is the most preferred tool in Boolean algebra. Truth table is a mathematical table specifically in connection with Boolean algebra, Boolean functions and propositional calculus. A mathematical table that displays all the possible truth values of a logical operation, is known as a truth table. It computes the functional values of logical expressions on each of their functional arguments.
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P | T(P) |
T | T |
F | T |
P | F(P) |
T | F |
F | F |
P | $\sim$P |
T | F |
F | T |
P | Q | (P$\wedge$Q) And |
T | T | T |
T | F | F |
F | T | F |
F | F | F |
P | Q | (P$\vee$Q) or |
T | T | T |
T | F | T |
F | T | T |
F | F | F |
P | Q | (P $\rightarrow$ Q) |
T | T | T |
T | F | F |
F | T | T |
F | F | T |
We can learn another logic operations with truth tables.The propositional logic truth tables are standard one.So we can't change the propositional value.
P | Q | (P$\wedge$Q) And |
T | T | F |
T | F | T |
F | T | T |
F | F | T |
P | Q | (P$\vee$Q) or |
T | T | F |
T | F | F |
F | T | F |
F | F | T |
The students can understand the propositional logic truth tables by using given example problems and they should practice the exercise problems.
Example 1: Find out the logical truth tables for given value using implication.
Input A: T T T F F T
Input B: T F F T T T
Solution:
A | B | Propositional value(P$\rightarrow$Q) |
T | T | T |
T | F | F |
T | F | F |
F | T | T |
F | T | T |
T | T | T |
The propositional A $\rightarrow$ B is T F F T T T.
Example 2: Find out the logical truth table for given values using conjunction.
Input A: F F T F T
Input B: F T T T F
Solution:
A | B | Propositional value(P$\wedge$Q) |
F | F | F |
F | T | F |
T | T | T |
F | T | F |
T | F | F |
The propositional A $\wedge$ B is F F T F F.
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