Define Truth Table Define Truth Table A truth table is a splitting up of a logic function in which we make a list of each and every one of the probable values the function can arrive at. A truth table characteristically consists of a number of columns and rows (similar to a simple table), in which the uppermost row corresponds to the logical variables (and sometimes their combinations), in proliferating complications set up to reach the final function. In representational logic, we frequently use letters to symbolize statements and the below mentioned symbols to stand for the connectives. Symbol
Connective
¬
NOT (Negation)
∧
AND (Logical conjunction)
∨
OR (Logical disjunction)
→
If ... Then (Conditional)
Know More About :- How to Find the Y Intercept of a Line
Tutorcircle.com
Page No. : 1/4
↔
If and only if (Bi - conditional)
We represent the values of a logic function with 1 and 0 or true (or T) and false (or F). Please note that we can use the notation 1 for either the truth - value or the false value. However, by convention, we use it as a truth - value. To understand the concept of truth table, let us draw a truth table for the negation function. A
¬A
T
F
F
T
This means that if the value of a statement is true, then its negation will be its false value and vice versa. ¬ A simply means not A. Logical conjunction and disjunction operations are of vital importance in discrete mathematics. Logical AND operation between two variables implies that the output value is true only when all the values are true otherwise it is false. The truth table of A ∧ B is given below. A
B
A∧B
T
T
T
T
F
F
F
T
F
F
F
F
Logical OR operation between two variables implies that the output value is true whenever one of the input values are true otherwise it is false. The truth table of A ∨ B is given below.
Learn More :- Perimeter of Square Calculator
Tutorcircle.com
Page No. : 2/4
A
B
A∧B
T
T
T
T
F
T
F
T
T
F
F
F
The conditional statement A → B is similar to the function (NOT A) OR B. A
B
¬A
¬ A ∧ B = A→ B
T
T
F
T
T
F
F
F
F
T
T
T
F
F
T
T
From the above truth table, we can note that we can form combinations to deduce complex logical functions’ truth tables. Bi – conditional logical operator symbolizes the true value when the input value of both the statements is true. The truth table for A ↔ B is given below: A
B
A↔B
T
T
T
T
F
F
Tutorcircle.com
Page No. : 2/3 Page No. : 3/4
Thank You For Watching
Presentation