Previous year gate paper Discrete Mathematics Gate 2025 Consider the following expressions.

Previous year gate paper Discrete Mathematics Gate 2025Consider the following expressions.

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Certainly! Let’s delve into a notable GATE CSE previous year question on Discrete Mathematics, specifically focusing on Propositional Logic:

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GATE CSE 2025 (Set 2) – Propositional Logic Question

Question:

Consider the following expressions:

1. (i) false

2. (ii) Q

3. (iii) true

4. (iv) P ∨ Q

5. (v) ¬Q ∨ P

How many of the above expressions are logically implied by the expression:
P ∧ (P ⇒ Q)?

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Solution:

We are given the expression:
P ∧ (P ⇒ Q)

Let’s analyze what this implies:

• P is true.

• P ⇒ Q is true.

From the implication P ⇒ Q, and knowing that P is true, it follows that Q must also be true. This is based on the truth table of implication, where the only case P ⇒ Q is false is when P is true and Q is false.

Therefore, from P ∧ (P ⇒ Q), we can deduce:

• P is true.

• Q is true.

Now, let’s evaluate each of the given expressions:

1. (i) false

   • This is a constant false value. Since we have deduced that both P and Q are true, we cannot conclude that false is implied.
     ⇒ Not implied

2. (ii) Q

   • We have deduced that Q is true.
     ⇒ Implied

3. (iii) true

   • A tautology; always true. Since our premises lead to true statements, this is trivially implied.
     ⇒ Implied

4. (iv) P ∨ Q

   • Since both P and Q are true, their disjunction is also true.
     ⇒ Implied

5. (v) ¬Q ∨ P

   • Let’s evaluate:

     • ¬Q is false (since Q is true).

     • P is true.

     • Therefore, ¬Q ∨ P = false ∨ true = true.
       ⇒ Implied

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Answer:

4 expressions are logically implied by P ∧ (P ⇒ Q):
(ii) Q, (iii) true, (iv) P ∨ Q, and (v) ¬Q ∨ P.

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Further Practice:

To strengthen your understanding of Discrete Mathematics for GATE, consider exploring the following resources:

• GeeksforGeeks – Discrete Mathematics GATE Questions: A comprehensive collection of previous year questions with explanations.

• Examside – Topic-wise GATE CSE Questions: Offers categorized questions for focused practice.

• PracticePaper – Discrete Mathematics for GATE CSE: Provides practice questions with solutions to test your knowledge.

Video Resources:

For a visual and in-depth explanation, you might find the following video helpful:

Feel free to explore these resources to enhance your preparation!

Previous year gate paper Discrete Mathematics Gate 2025 Consider the following expressions.