Table of Contents
What is the Truth Table?
A truth table is a mathematical table used in logic to determine the truth values of logical propositions. The truth table for a proposition consists of a series of rows and columns. The row and column headings correspond to the propositional variables in the proposition. The table is filled in with the truth values of the proposition for all possible combinations of the truth values of the propositional variables.
Truth Table for Binary Operations
The table below shows the truth table for binary operations (AND, OR, and NOT).
Binary Operation
Truth Table
AND
OR
NOT
T
F
T
F
T
F
T
F
T
F
T
F
F
T
F
T
F
T
F
T
NOR and OR Truth Table Operation
NOR gate is a digital logic gate that implements logical NOR operation, and is a combination of an AND gate and an OR gate. The output of a NOR gate is TRUE only when both inputs are FALSE.
OR gate is a digital logic gate that implements logical OR operation, and is a combination of an AND gate and an OR gate. The output of an OR gate is TRUE when either input is TRUE.
NAND and AND Operational True Table
NAND
A B
0 0
0 1
1 0
1 1
AND
A B
0 0
0 1
0 0
1 0
1 1
XOR Operation Truth Table
Input 1 Output 1 Input 2 Output 2
0 0 0
0 1 1
1 0 1
1 1 0
Conditional and Biconditional Truth Tables
The following truth tables show the truth values of conditional and biconditional statements.
Conditional
p → q
T T T
T F F
F T T
F F F
Biconditional
p ↔ q
T T T
T F F
F T T
F F F
Conditional Truth Table
p q ¬p
¬p
T T F
F T
F F T
T F
Biconditional Truth Table
A biconditional is a statement of the form “If A, then B” and “If B, then A”. The truth table for a biconditional is shown below.
A B A → B B → A T T T T F F F T
Importance of Learning the Truth Table for Binary Operations
The truth table for binary operations is important because it helps us to understand the logical relationships between the operands. This understanding can be helpful when solving problems or when writing logic diagrams.
How to Learn the Truth Table for Binary Operations
To learn the truth table for binary operations, one must first understand the concept of a truth table. A truth table is a way of displaying all the possible outcomes of a logical operation. The table will have one column for each input and one column for each output. The table will also have a row for each combination of inputs. In the binary operations column, the table will list the possible outcomes of each operation when both inputs are either 0 or 1.
