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Proofs in Mathematics > Introduction

Introduction

In our daily lives, we come across numerous statements. We assess their validity, accepting some as true and dismissing others. However, there are times when we are uncertain about a statement's truthfulness. How do we determine whether a statement is true or false?

For instance, in a financial dispute regarding loans or debts, simply claiming that a bank owes you money is not enough. You must provide supporting documents as evidence of the transaction; otherwise, people would not believe you. Similarly, if we analyze our daily conversations, we often accept statements without verification. While this may be common in everyday life, mathematics requires a more rigorous approach—every statement must be examined and proven either true or false.

Consider the following statements:

The sun rises in the east.

3+2=5

New York is the capital of the USA.

4>8

How many siblings do you have?

Goa has a better football team than Bengal.

A rectangle has four lines of symmetry.

x+2=7

Please come in.

What is the probability of getting two consecutive sixes when rolling a six-sided die?

How are you?

The sun is not stationary but moves at high speed all the time.

x< y

Where do you live?

Some of these statements are , such as 4>8 and "New York is the capital of the USA.". Others are , like "The sun rises in the east" and mathematical facts like 3+2=5.

Additionally, some statements are conditionally true, meaning they are only valid for certain cases. For example, x+2=7 is only true when x = , and x < y depends on the specific values of x and y.