Day 04 part 04- Discrete mathematics for computer science Negation Operator of Proposition

Day 04 part 04- Discrete mathematics for computer science Negation Operator of Proposition

The Negation Operator (¬) in Propositional Logic is one of the fundamental logical operators in Discrete Mathematics. It is used to reverse the truth value of a given proposition.

Definition:

If P is a proposition, then the negation of P, denoted as ¬P, is a proposition that is true when P is false and false when P is true.

Truth Table of Negation Operator (¬P):

Example:

1. Let P = “It is raining.”

   • Then, ¬P = “It is not raining.”

2. If P = “5 is greater than 3” (which is true),

   • Then, ¬P = “5 is not greater than 3” (which is false).

Properties of Negation Operator:

• Double Negation: ¬(¬P) = P
• Involutory Property: Applying negation twice brings the original value back.

Would you like more examples or explanations related to propositional logic?

Day 04 part 04- Discrete mathematics for computer science Negation Operator of Proposition

Discrete Mathematics for Computer Science Prof. Raissa D …

Discrete Mathematics and Its Applications, Eighth Edition

In Discrete Mathematics, particularly in Propositional Logic, the Negation Operator (denoted as ¬ or ~) is a fundamental unary operator that inverts the truth value of a given proposition.

What is Negation?

If p is a proposition, then its negation, denoted as ¬p, is the statement “It is not the case that p.” This operation flips the truth value of the original proposition.

Truth Table:

Example:

• Let p: “It is raining.”

• Then, ¬p: “It is not raining.”

This means if p is true (it is indeed raining), then ¬p is false, and vice versa.

Key Properties of Negation

1. Double Negation:

   • Negating a negation returns the original proposition. That is, ¬(¬p) ≡ p.ggc-discrete-math.github.io

2. De Morgan’s Laws:

   • These laws relate the negation of conjunctions and disjunctions:

     • ¬(p ∧ q) ≡ (¬p) ∨ (¬q)

     • ¬(p ∨ q) ≡ (¬p) ∧ (¬q)

   These equivalences are crucial for simplifying logical expressions and are widely used in computer science and digital logic design.

Further Learning

For a more in-depth understanding, you might find the following video helpful:

Feel free to ask if you’d like this explanation in Hindi or need further examples!

Day 04 part 04- Discrete mathematics for computer science Negation Operator of Proposition