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Mathematical Logic

Mathematical logic is quite useful in understanding and developing insight about different concepts of maths. Logic in mathematics is actually refers to mathematical reasoning. The operators representing mathematical logics are called logical operators. There are three basic logics in maths -

  • Conjunction
  • Disjunction
  • Negative
We shall discuss each in detail.

Conjunction (AND): Conjunction or AND is a logical operator that is applied between two statements and is true when both statements are true. Conjunction is written as AND and is symbolically denoted by "$\wedge$". A statement "A $\wedge$ B" indicates that this statement will be true when both A and B are true. If one of them is false, A ^ B will also be false.

The pictorial representation of a logical operator with all possible inputs is known as truth table. The truth table of conjunction is given below:
 A 
 B 
 A $\wedge$ B 
 T  T  T
 T  F  F
 F  T  F
 F  F  F

It is a binary operator which means there are two input values.

Disjunction (OR): The logical operator disjunction is also applied between two statements. It is true when either at least one of the statements is true or both of them are true. Disjunction or OR is represented by the symbol "$\vee$". A statement "A $\vee$ B" describes that this statement is true when either A or B is true or both are true. It is false only when both the statements are false.

The truth table of disnjunction is given below:
 A 
 B 
 A $\vee$ B 
 T  T  T
 T  F  T
 F  T  T
 F  F  F

It is also a binary operator.

Negation (NOT): Negation, as the name suggests, negates the statement which means it result it opposite to the given statement. It is denoted by NOT or by a "$\sim$" symbol before the statement. If a statement is true, then its negation gives false value and if it is false, then its negation gives true value. Truth table of negation is shown below:

   A   
$\sim$A
F
F
T

It is a unary operator which means there is only one input.

Related Calculators
Logic Truth Table Calculator Mathematical Equation Solver
 

More topics in  Mathematical Logic
Logical Operators
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