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
Additionally, some statements are conditionally true, meaning they are only valid for certain cases. For example, x+2=7 is only true when x =