Tautology - Always True Statements
Summary
A tautology is a statement that doesn’t leave room for doubt; it’s a truth that remains steadfast regardless of the circumstances.
A tautology is a statement that is always true, regardless of the truth values of its individual components. In other words, it’s a statement that holds true under all possible conditions.
Explanation
Imagine a statement that, no matter what, will never lead to a false conclusion. This statement is a tautology. Tautologies are like logical facts that stand solid, unwavering against any combination of true or false values.
Example
Consider the statement: “Either it’s raining, or it’s not raining.” This statement is a tautology because, in any situation, it’s either raining or it’s not, making the entire statement always true.
Another example is the statement: “A circle is a shape with a curved boundary equidistant from its center.” This is a tautology as it defines a circle in a way that is always true for any object referred to as a circle.
Key Points
- Tautologies provide certainty and are considered inherently true.
- They are common in logical reasoning and mathematics.
- The structure of a tautology ensures that the truth of the statement is guaranteed.