Truth Table

In math, a truth table is used to conduct logical operations. Boolean algebra or boolean functions are the operations that make up these operations. Its main purpose is to determine whether a propositional phrase is true or false based on the supplied values. The basis for this is boolean algebra. It has one or more columns for input values, such as P and Q, and one allocated column for output results. The outcome of the unary or binary operation performed on the provided input values is the output we get here. AND, OR, NOR, XOR, XNOR, and other binary operations are examples. All the different types of operations will be discussed here, along with their corresponding truth tables with truth values.

Truth table for unary operator

Unary has only one input, which can be either True or False. There are four unary operations for these inputs, which we will conduct here. They are as follows:

• Logical True (Only True)

• Logical false (Only False)

• Logical Identity ( Same value )

• Logical negotiation ( Opposite value )

Logical true

Regardless of the input value, the output of this operation is always true. If P represents the input values and Q represents the output, the table can be written as follows : 

In the given table T is used for the value ‘ truth ’ and F is used for the value ‘ false ’.

Logical false

Regardless of the input value, the output of this operation is always False. If P represents the input values and Q represents the output, the table can be written as follows :

In the given table T is used for the value ‘ truth ’ and F is used for the value ‘ false ’.

Logical identity

Regardless of the input value, the output of this operation is always the same as the given input. If P represents the input values and Q represents the output, the table can be written as follows :

In the given table T is used for the value ‘ truth ’ and F is used for the value ‘ false ’.

Logical negotiation

When we apply the logical negotiation operation on a single logical value or propositional value, the output value is the inverse of the input value. Let us have a look at the truth table for this:

In the given table T is used for the value ‘ truth ’ and F is used for the value ‘ false ’.

Truth table for binary operation

Two variables for input values make up the binary operation. The output result will also be depending on the operation performed on the input or proposition values, and it will be either True or False. The following are some of the most common binary operations:

• AND

• OR

• NAND

• NOR

• XOR

In the given table T is used for the value ‘ truth ’ and F is used for the value ‘ false ’.

AND and NAND operator

As you can see from the table, the output of the AND operation is True only if both input values are true; otherwise, the output is false. The sign ( ^ ) stands for the AND operator.

The negation of the AND operation yields the NAND output result, which is denoted by ( ~^ ).

OR and NOR operator

If either of the two input values is True, the output result is always TRUE, according to the OR statement. The symbol ( V ) is used to represent it.

The NOR operation, on the other hand, produces the output, but the OR operation does not. It indicates that for NOR, the assertion that is True for OR is False. And it is written as ( ~V ).

XOR operator

The table specifies that the input values must be absolutely true or false. XOR is represented by the symbol ( ⊻ ).

Conclusion 

In math, a truth table is used to conduct logical operations. Boolean algebra or boolean functions are the operations that are used to perform some operations. Its main purpose is to determine whether a propositional phrase is true or false based on the supplied values. The basis for this is boolean algebra. It has more than one column as input values, such as P and Q, and one allocated column for the output results. The outcome of the unary or binary operation performed on the provided input values is the output we get here. Some of the examples of the binary operators are AND, OR, NOR, XOR, XNOR etc.