Types of Reasoning Statement in Maths

Types of Mathematical Reasoning Statements

Value of a statement

Simple statement: Simple statements are those statements whose truth value does not explicitly depend on another statement. They are direct and does not include any modifier.

Example:

‘364 is an even number’

Compound statement: When two or more simple statements are combined using words ‘and’, ‘or’, ‘if…then’, and ‘if and only if’ then the resultant statement is known as a compound statement. ‘and’, ‘or’, ‘if…then’, and ‘if and only if’ these are also called as logical connectives.

Example:

‘ I am studying psychology and history’.

Elementary operation of logic:

Conjunction: When a compound statement is created using ‘and’ is known as a conjunction.

a ^ b

Here, a and b are two simple statements.

Disjunction: When a compound statement is created using ‘or’ is known as disjunction.

a v b

Here, a and b are two simple statements.

Conditional statement: When a statement is created by connection two simple statements using ‘if….then’ is known as conditional statement.

a → b

Here, a and b are two simple statements.

Biconditional statement: When a statement is created by connection two simple statements using ‘if and only if’ is known as biconditional statement.

a ↔ b

Here, a and b are two simple statements.

Negation: When a statement is created by using words like ‘no’, ‘not’ is known as negation.

~a

Examples:

Are the following sentences statements? answer in true or false

(i) ”7 + 5 = 19”

This statement will be considered false because the addition is not correct

(ii) “today’s weather is very nice”

This statement is neither true nor false because if the weather seems nice to one person it does not mean that every person will share the same opinion.

(iii)” 2 + 5 – 3 + 2 = 6 ”

This statement will be considered true because the equation is correct.

(iv) harsh is very nice

False, because this is an opinion of a person and opinions can vary.

(v) 7 + 5 = 21

False, this will compute to 12 but the answer is given 21 so the answer is false.

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