Profile
Settings
Refer your friends
Sign out
In boolean algebra, the truth table is a mathematical table showing all the truth values of the statement for basically each combination of true values for all the component statements. A statement is known as a sentence that has one and only one of the given two values that are possible. There are different types of tables for operations like unary operations, binary operations, and logical operations. Truth tables give you true or false, given by the symbol T for True and F for false at times except for T or F; it is also denoted by 1 or 0. As only two values can be denoted, it is also called two-valued logic.
Truth Table for unary operations:
Truth Table is used to construct truth tables for its component statements. In unary operations, logical operations are generally those operations that only have one logical variable.
The truth table for logical true:
For logical true, it will only return the value true despite whatever the input is.
The truth table for logical false:
For logical false, it will only return the value false despite whatever the input is.
The truth table for negation:
Logical negation is a kind of operation that returns the opposite value of the input. If the input is true, output will be false, and output will be true if the input is false, also known as not. The truth table for negation is given below:
Truth Table for binary operations:
These include two variables that we must put as an input value. The output will be dependent on the input values that can be either true or false. Some of the major binary operations are
NOR and OR operation
NAND and AND operation
Conditional and Biconditional
XOR.
The input value will be mentioned as X and Y. Here, T is for true, whereas F stands for false.
NOR and OR operation:
NOR and OR operations are opposite of each other. However,
For OR operations, if any of the two input values are true. The output will always be true; if one of the inputs is true, the output is considered true. The output will always be false if one of the inputs is false.
NOR operations are completely contradictory to OR operations. This operation will be the opposite of that of the OR operation. If the output is true for OR, it will be False for NOR.
NAND and AND operation:
For AND operations, the output will only be true if both the input values are true else false. For NAND operations, the output is the opposite of AND, which means if the output of AND is true, the output for NAND will be false.
XOR operation:
The output of XOR operations is only true if one of the inputs is true. The output is false if both the input values are true or false.
Conditional operation:
A conditional operation is a logical statement; a statement p is called antecedent will imply statement q, called the consequent.
A conditional operational statement is written as p → q, translated to if p then q.
Biconditional Operation:
These work on if and only if statements, generally called iff, which simply means p and q are interchangeable statements. If one is true, you will automatically know the other one is true. If one is false, the other must also be false.
Logical Operations:
The logic tables operations with the truth table will be discussed, but the proposition value of truth tables will be logical, so we can not change the value.
There are a few steps to solve logical operations:
- First is to Solve parentheses if given
- After that, we have to solve the NOT operator
- And after this, the AND operator
- The last step is to solve the OR operator
Conclusion:
A truth table is a mathematical tab; statistics analyse statements or arguments to determine whether they are logical or true. It displays the logical operations or input signals in the form of a table. The truth table identifies all the possible combinations of input and output. It has a row for every combination or prescribes the value of the function, either 0 or 1. There are different types of tables for operations like unary operations, binary operations, and logical operations. Truth tables give you true or false, given by the symbol T for True and F for false at times except for T or F; it is also denoted by 1 or 0.
