JNTU
JNTU B.Tech II DISCRETE MATHEMATICS Previous Question Paper (August/September - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
State and prove De-Morgan’s Law using truth tables.
Answer
De Morgan's Laws state that for any two propositions p and q:
Truth Table Proof:
| p | q | p ∧ q | ¬(p ∧ q) | ¬p | ¬q | ¬p ∨ ¬q |
|---|---|---|---|---|---|---|
| T | T | T | F | F | F | F |
| T | F | F | T | F | T | T |
| F | T | F | T | T | F | T |
| F | F | F | T | T | T | T |
Since the columns for ¬(p ∧ q) and ¬p ∨ ¬q are identical, the first law is proven. A similar table comparing ¬(p ∨ q) and ¬p ∧ ¬q yields identical truth values, proving the second law.
Write down the contrapositive, the converse, and the inverse of the conditional statement: “If the sky is cloudy then it will rain or it will not rain”.
Answer
Let p be "the sky is cloudy" and q be "it will rain". The original conditional statement is p → (q ∨ ¬q).
The Contrapositive is: If it is not the case that it will rain or it will not rain, then the sky is not cloudy.
The Converse is: If it will rain or it will not rain, then the sky is cloudy.
The Inverse is: If the sky is not cloudy, then it will not rain and it will rain.
Find the PDNF and PCNF by constructing the truth table for the expression:
Answer
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Draw the Hasse diagram for the Poset (P(S), /), where S={2, 3, 4, 5, 6, 10, 12, 20, 25} and P(S) is the power set of S.
Answer
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Draw the Venn diagrams for each of these combinations of the sets A, B, C, and D: i) (A ∩ B) ∪ (C ∩ D) ii) A ∪ (B ∩ C ∩ D)
Answer
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Using Substitution method and master theorem solve the following recurrence relation:
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What is Inclusion-Exclusion principle? Write down the applications of inclusion and exclusion.
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Using generating function, solve the
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Define planar graph. Mention its structural properties.
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Discuss graph coloring problem in brief.
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What is a tree? Explain various graph traversal techniques with illustrative examples.
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