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

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

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 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 (∧)

P	Q	P ∧ Q
T	T	T
T	F	F
F	T	F
F	F	F

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.

Would you like more examples or practice questions?

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

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