Mathematical Logic
In this page we are going to discuss about mathematical logic concept .Logic means reasoning. Reasoning may be legal opinion or mathematical confirmations. We apply certain logics in mathematics. Basic Mathematical logics are Negation, Conjunction and disjunction. Symbolic form of mathematical logics are, ‘~’ for negation '`^^`' for Conjunction and ' V ' for disjunction.We use this logcs in physics there it is represented as AND, OR and NOT respectively. Truth table states the relation between the compound statement and sub – statement. Let us see symbolic logic truth tables in this article.In physics it is called as logic gates. A logic gate is simply an electronic circuit which operates on one or more input to produce an output.
There are three types of logic operators :
- Negation (NOT)
- Disjunction (OR)
- Conjunction (AND)
NEGATION
Negation is an operator which gives the opposite statement of the previous statement. It is also known as NOT. It is an operation who gives the opposite result. If input is true then output is false. If input is false then output is true. It has one input and one output.
Examples for negation
Problem 1 : This year is a leap year.
Solution: This year is not a leap year.
Problem 2: Amar is taller than Vivek.
Solution: Amar is not taller than Vivek.
True table foe NOT :
| Input(P) | Output(~P) |
| T | F |
| F | T |
DISJUNCTION
We can join two statement by “OR” operand. It is also known as Disjunction. It symbolic from is ‘V’ .In this operator If any one of the statement is true then result is true, and If both the statement is false then result will we false. It has two or more input but only one output.
True Table for OR :
| Input | Input | Output |
| P | Q | P OR Q |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Example of disjunction
Problem:
Find the truth value for the following statements:
A: 18+1 =19
B: 180+1 = 1801
Solution:
The given statements are
A: 10 + 1 = 11
B: 18 + 1 = 181
In this the statement A is true and the statement B is false.
| A | B | AvB |
| T | F | T |
The disjunction of a compound statement is only false if both the combining statements are false else the disjunction is true.
CONJUNCTION
We can join two statement by “AND” operand. It is also known as Conjunction. It symbolic from is ‘?’ .In this operator If any one of the statement is false then result is false, and If both the statement is true then result will we true. It has two or more input but only one output.
Ture table for AND (Conjunction):
| Input | Input | Output |
| P | Q | P AND Q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Example for Conjunction
Problem: Find the truth value for the following statements:
A: 18+1 =19
B: 180+1 = 1801
Solution:
The given statements are
A: 10 + 1 = 11
B: 18 + 1 = 181
In this the statement A is true and the statement B is false.
| A | B | AvB |
| T | F | F |
The conjunction of a compound statement is only true if both the combining statements are true else the conjunction is false.
| More topics in Mathematical Logic | |
| Negation | Conjunction |
| Disjunction | Conditional |
| Compound Statement | Bi Conditional Statements |
| Tautologies | Truth Table |
| Equivalence Statements | Directional Derivatives |
