. Statement based Problem on Proposition- GATE 2025 Discrete Consider the following statements

. Statement based Problem on Proposition- GATE 2025 Discrete Consider the following statements

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कृपया पूरा प्रश्न साझा करें ताकि मैं GATE 2025 Discrete Mathematics (Propositional Logic) के Statement-based Problem को हल करने में आपकी मदद कर सकूँ।

अगर यह तार्किक कथनों (Logical Statements), सत्य सारणी (Truth Table), परिणाम (Implication) या तार्किक प्रमेय (Logical Theorems) से संबंधित है, तो मैं विस्तृत हल और व्याख्या दे सकता हूँ।

. Statement based Problem on Proposition- GATE 2025 Discrete Consider the following statements

Information Brochure – GATE 2025 – IIT Roorkee

Discrete Mathematics for Computer Science

Here’s a sample Statement-based Problem on Propositions (Logic) in Discrete Mathematics, commonly seen in GATE exams (like GATE 2025). These questions test your understanding of propositional logic, truth values, and logical equivalence.

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Sample GATE-Style Question on Proposition

Question:
Consider the following two statements:

• P: If it rains, then the ground gets wet.

• Q: The ground is not wet.

Which of the following conclusions is logically valid?

A. It did not rain
B. It rained
C. It rained and the ground is dry
D. Nothing can be concluded

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Solution:

Convert the statements into propositional logic:

• Let R = “It rains”

• Let W = “The ground gets wet”

So,

• P: $R\to W$

• Q: $\neg W$

From P and Q, can we infer anything?

From logic:

• $R\to W$ and $\neg W$
  ⟹ By Contrapositive Rule, $\neg W\to \neg R$

So, $\neg R$ is true.

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Correct Answer: A. It did not rain

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Tips for Solving These in GATE:

• Convert English sentences to propositional logic

• Use rules like contrapositive, modus ponens, modus tollens

• Carefully identify assumptions vs. conclusions

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Would you like more such GATE-style problems with explanations in Hindi, or a PDF worksheet of practice questions?