QB DSGT Internal assessment 1.pdf

Indala College of Engineering Department of Computer Engineering Question Bank Discrete structure and Graph Theory 1. What is a tautology? Check whether the following logical express...

Indala College of Engineering Department of Computer Engineering Question Bank Discrete structure and Graph Theory 1. What is a tautology? Check whether the following logical expression is tautology? [(p→r) ^ (~q→p) ^ ~r ] → q (p→Q)↔(~q→~p) [(A→B)ꓥ ~q]→~p) 2. Convert the following into CNF form. (A→B) → ((B→C) →(A→C)) 3. Explain two different types of Quantifiers with example? 4. Let the Univaersal Set U={1,2,3,4…..10), A={2,4,7,9} , B={1,4,6,7,10}, C={3,5,7,9} find AUB 2) B ∩ C 3) (A ∩ B) UC 4) (BUC)∩C 5. Translate each of the following in verbal language P: Teacher is Present Q: Student attend the class a. i)pVq ii)P↔q iii)pꓥq iv)q↔p 6. Which of the following statement tautology, Contradiction & Contingency 1)(qVp)V(qꓥ~p) 2)(pVq)V(~pVq) 3)(pꓥ~p) 7. Explain inference and the Rules of Inference for predicates in detail each with respective example. 8. Define Set. Explain any 3 set operations in brief with respective example with the help of venn diagram. 9. Show that using AU(B~∩C) = (AUB~)∩(AUC) venn diagram. 10. Let A={1,2,3,4,8}, B={1,4,6,9} Let aRb if a\b (a divides b) find the relation matrix. Let A={a,b,c,d) 11. Let A={1,2,3,4} and R={(1,2),(2,),(1,3),(3,2)} find the transitive closure of r by Warshall’s algorithm. 12. Explain Equivalence Relation with their respective Property and suitable example