Value of a statement
A statement if is either correct or incorrect or true or false. The true or false state of a statement is known as a truth value. If the statement is false it is determined as ‘F’ and if the statement is true it is determined as ‘T’.
Example:
(i) ‘364 is an even number’ is T because this statement is true.
(ii) ’71is divisible by 2′ is F because this statement is false.
Truth table:
As we know that a statement can be true or false and these values are known as truth values. So, a truth table is a summary of the truth values of the resultant statement for all possible combinations of truth values of component statements.
In the case of n number of statements, there are 2n distinct possible arrangements of truth values in the table of the statements. In the truth table, when the compound statement is true for every condition then it is known as a tautology, and when the compound statement is false for every condition is known as a fallacy.
Example:
The truth table for one statement ‘p’ will be written as:
p T F The truth table of two statements ‘p’ and ‘q’ will be taken as:
p q p ^ q T T T T F F F T F F F F
Statements – Mathematical Reasoning
Statements – Mathematical Reasoning: The study of logic through mathematical symbols is called mathematical reasoning. Mathematical logic is also known as Boolean logic. In other words, in mathematical reasoning, we determine the statement’s truth value.
Table of Content
- What is Mathematical Reasoning?
- Statements in Mathematical Logic
- Types of Mathematical Reasoning Statements
- Inductive Reasoning
- Abductive Reasoning
- Analytical Reasoning
- Critical Reasoning
- Constructive Reasoning
- Geometric Reasoning
- Probabilistic Reasoning
- Types of Reasoning Statement in Maths
- Value of a statement
- New Statements from Old Statement