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Day 04Part 06- Discrete mathematics for computer science – Dis-junction Operator of proposition.

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Day 04Part 06- Discrete mathematics for computer science – Dis-junction Operator of proposition.

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Disjunction Operator (∨) in Propositional Logic – Discrete Mathematics for Computer Science

In propositional logic, the disjunction operator (∨) represents the logical “OR” operation. It is used to form compound statements that are true if at least one of the given propositions is true.

1. Definition of Disjunction (∨)

Truth Table for Disjunction (P ∨ Q):

P Q P ∨ Q
T T T
T F T
F T T
F F F

2. Symbolic Representation

3. Key Properties of Disjunction (∨)

(A) Commutative Property:

P∨Q=Q∨PP ∨ Q = Q ∨ P

 Example: “It is raining OR it is cloudy” is the same as “It is cloudy OR it is raining.”

(B) Associative Property:

(P∨Q)∨R=P∨(Q∨R)(P ∨ Q) ∨ R = P ∨ (Q ∨ R)

 Example: If P = “Hot”, Q = “Cold”, and R = “Windy”, the order in which we group them doesn’t change the truth.

(C) Identity Law:

P∨False=PP ∨ \text{False} = P

 Example: “It is sunny OR False” → The truth value remains that of “It is sunny.”

(D) Domination Law:

P∨True=TrueP ∨ \text{True} = \text{True}

 Example: “It is sunny OR True” → Always True.

(E) Idempotent Law:

P∨P=PP ∨ P = P

 Example: “It is raining OR it is raining” → No change in truth value.

(F) Distributive Law:

P∨(Q∧R)=(P∨Q)∧(P∨R)P ∨ (Q ∧ R) = (P ∨ Q) ∧ (P ∨ R)

4. Application in Computer Science

5. Disjunction in Logic Gates

A B A OR B
0 0 0
0 1 1
1 0 1
1 1 1

Conclusion

Would you like more examples or practice problems on this topic?

Day 04Part 06- Discrete mathematics for computer science – Dis-junction Operator of proposition.

Discrete Mathematics for Computer Science Prof. Raissa D …

Propositional Logic Discrete Mathematics

Here’s a clear and concise explanation for:

Day 04 Part 06 – Discrete Mathematics for Computer Science: Disjunction Operator of a Proposition

What is a Disjunction?

In propositional logic, a disjunction is a logical operation that joins two propositions using the “OR” operator.

Symbol:

∨ (called “vee”)

Expression Format:

If P and Q are propositions, then:

P ∨ Q means “P or Q“

Truth Table of Disjunction (P ∨ Q):

P Q P ∨ Q
T T T
T F T
F T T
F F F

Key Idea: The disjunction is true if at least one of the propositions is true.

Example:

Let:

Then:
P ∨ Q = “It is raining or it is snowing”

This statement is true if either raining, snowing, or both.

Disjunction in Programming Terms:

Many programming languages use:

Example in C, Java, Python (using or):

python
P = True
Q = False
print(P or Q) # Output: True

Summary:

Let me know if you’d like practice problems, diagrams, or code-based applications of disjunction.

Day 04Part 06- Discrete mathematics for computer science – Dis-junction Operator of proposition.

Discrete Mathematics for Computer Science