Logical equivalence facts for kids
Two statements are logically equivalent if they always mean the same thing. This means that if one statement is true, the other one is also true. And if one is false, the other is false too. They have the same "truth value" in every situation.
Think of it like this: If you say, "It is raining AND the sun is shining," and someone else says, "The sun is shining AND it is raining," both statements mean the exact same thing. They are logically equivalent because the order doesn't change the meaning.
In logic and mathematics, we use special symbols to show that two statements are logically equivalent, like 
, 
, or 
.
Contents
What is Logical Equivalence?
Logical equivalence is a big idea in logic. It helps us understand when different ways of saying something actually mean the same thing. This is super useful in mathematics, computer science, and even everyday arguments.
How Do We Know if Statements are Equivalent?
One way to check if two statements are logically equivalent is by using something called a truth table. A truth table lists all possible ways a statement can be true or false. If two statements have identical truth tables, they are logically equivalent.
For example, let's say:
- P means "It is cold."
- Q means "It is snowing."
The statement "P and Q" means "It is cold AND it is snowing." The statement "Q and P" means "It is snowing AND it is cold."
No matter if it's cold, snowing, both, or neither, these two statements will always have the same truth value. If one is true, the other is true. If one is false, the other is false. So, they are logically equivalent.
"If and Only If" Statements
When two statements, let's call them P and Q, are logically equivalent, we can say "P if and only if Q." This phrase means that P is true exactly when Q is true, and P is false exactly when Q is false. It's a very strong connection between two ideas.
When a statement like "P if and only if Q" is always true because P and Q are logically equivalent, we call it a tautology. A tautology is a statement that is always true, no matter what.
Related pages
See also
In Spanish: Equivalencia lógica para niños
