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Proofs in Mathematics

    Introduction

    Mathematical Statements

    Verifying The Statements

    Reasoning in Mathematics

    Theorems, Conjectures And Axioms

    What is a Mathematical Proof?

    Exercise 15.1

    Exercise 15.2

    Exercise 15.3

    Exercise 15.4

    What We Have Discussed

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Proofs in Mathematics > Mathematical Statements

Mathematical Statements

A statement is a sentence that is either true or false, but not both. While we can create countless sentences in any language, not all of them qualify as statements. Let's understand this better:

Non-Statements

Questions (e.g., "Where do you live?")

Commands (e.g., "Please come in")

Exclamations

Ambiguous sentences

Mathematical statements must be precise and unambiguous. They must have exactly one truth value - either true or false.

Let's analyze if the following are statements:

"3 is a prime number" : This a statement and it is

"Product of two odd integers is even" : This a statement and it is

"For any real number x, 4x + x = 5x" : This a statement and it is

"The Earth has one moon" : This a statement and it is

"Ramu is a good driver" : This a statement

"Bhaskara has written a book 'Leelavathi'" : This a statement and it is

"All even numbers are composite" : This a statement and it is as is even and .

"x > 7": This a statement only when x is specified.

"A rhombus is a square" : This a statement and it is

"4 and 5 are relative primes" : This a statement and it is