Day 04Part 07-Discrete mathematics for computer science-Conjunction operator of proposition example.

 Day 04 Part 07 – Discrete Mathematics for Computer Science

 Conjunction Operator (AND) in Propositional Logic

In Propositional Logic, the Conjunction (∧) operator is used to combine two propositions, and the result is true only if both propositions are true.

 Definition of Conjunction (∧) Operator

Let P and Q be two propositions. The conjunction of P and Q (denoted as P ∧ Q) is true only when both P and Q are true.

 Truth Table for Conjunction (∧)

Key Point: Conjunction results in true (T) only if both inputs are true. Otherwise, the result is false.

 Example of Conjunction Operator (∧)

Example 1:

Let:

• P: “It is raining.”
• Q: “I have an umbrella.”

If we use the conjunction operator, we get:
P ∧ Q = “It is raining AND I have an umbrella.”

• If both statements are true, the result is true.
• If either P or Q is false, the result is false.

 Application of Conjunction in Computer Science

Boolean Logic in Programming

Here, accessGranted() executes only if both conditions are true.

Circuit Design (AND Gate)

• Used in logic circuits where both inputs must be 1 for output to be 1.

 Conclusion

 The Conjunction (AND) operator is widely used in logic, programming, and digital circuits.
 It ensures that both conditions must be true for an action or output to be true.

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Day 04Part 07-Discrete mathematics for computer science-Conjunction operator of proposition example.

Discrete Mathematics for Computer Science Prof. Raissa D …

Propositional Logic | Discrete Mathematics

Propositional Logic Discrete Mathematics

Discrete Mathematics for Computer Science

DISCRETE MATHEMATICS

Here’s a clear and simple explanation of:

Day 04 Part 07 – Discrete Mathematics: Conjunction Operator of Proposition with Example

What is a Proposition?

A proposition is a statement that is either true (T) or false (F) — but not both.

Examples of propositions:

• “It is raining.” (True or False)
• “5 > 3” (True)
• “x + 2 = 7” (Not a proposition unless x is known)

What is Conjunction (AND Operator ∧)?

Conjunction is a logical operator that combines two propositions.
It is represented by the symbol ∧ and is read as “AND”.

If P and Q are two propositions, then the conjunction is:

P ∧ Q → “P AND Q”

Truth Table for Conjunction (P ∧ Q):

Conclusion:
Conjunction is true only when both P and Q are true.

Example 1:

Let:

• P: “It is Sunday” → T
• Q: “The school is closed” → T

Then:
P ∧ Q = “It is Sunday AND the school is closed”
This is true.

Example 2:

Let:

• P: “It is raining” → T
• Q: “The sun is shining” → F

Then:
P ∧ Q = “It is raining AND the sun is shining”
This is false (because both are not true)

Visual Summary:

P:     Q:     → P ∧ Q:   
P:     Q:     → P ∧ Q:   
P:     Q:     → P ∧ Q:   
P:     Q:     → P ∧ Q: 

Key Points to Remember:

• Conjunction (AND) requires both propositions to be true.
• It is fundamental in logic gates, proofs, and digital circuits.

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Day 04Part 07-Discrete mathematics for computer science-Conjunction operator of proposition example.

UNIT – I–DISCRETE MATHEMATICS – SMT1304