≡Logical Equivalence
What is it?
It is when two different sentences have exactly the same logical value.
👉 That means:
Even if the sentence changes, the final result (T or F) does not change.
Main idea
If two expressions:
always give the same result in the truth table
➡️ then they are equivalent
📍 Simple example
“Not (A and B)”
“Not A or Not B”
👉 Both expressions are logically the same, even if they look different.
De Morgan’s Laws
De Morgan’s Laws explain how to negate expressions with AND and OR.
They are one of the most important and frequently tested topics in Logic.
1st De Morgan Law
Negation of “AND (∧)”
Not (A and B)
Not A or Not B
👉 When you negate an “AND”, it becomes “OR”
👉 And you negate each part
Example:
“Not (it is raining AND it is cold)”
“It is not raining OR it is not cold”
2nd De Morgan Law
Negation of “OR (∨)”
Not (A or B)
Not A and Not B
👉 When you negate an “OR”, it becomes “AND”
👉 And you negate each part
Example:
“Not (I am studying OR I am working)”
“I am not studying AND I am not working”
How to understand it easily
🔄 Golden rule:
“AND” becomes “OR”
“OR” becomes “AND”
Everything is negated
Most common mistake in exams
Thinking you only negate the first term
Wrong example:
“Not (A and B)” → “Not A and B” ❌
✔️ Correct:
“Not A or Not B”
Did you know?
