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

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

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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):

P ¬P
T F
F T

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:

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:

p ¬p
True False
False True

Example:

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