In this post, we have listed the Assignment [1] AND Assignment[2], II B.Tech CSE (NR23 Regulation). These questions are prepared from college lecture notes and are useful for assignments, mid exams, and sem exams.

 CLICK THIS FOR ASSIGNMENT 1 Q&A

CLICK THIS FOR ASSIGNMENT 2 Q&A

QUESTIONS:
ASSIGNMENT 1:
1. Show that (p→ (q  r)) ↔ ((p→ q) ʌ (p→ r)) is a Tautology.
2. Prove that (r→ (p→ q)) and ((p → (q r)) are equivalent.
3. Write converse, inverse, contrapositive for the given statement
“If it rains then the match will be cancelled”
4. Find DNF and CNF of (p→ q) ʌ (p ʌ q)
5. Find the PDNF & PCNF of (P Λ Q) V (P Λ R) V (Q Λ R).
6. S.T the set of premises p→ q, p→ r, q→ r, p is inconsistent.
7. S.T the conclusion C follows from H1, H2 and H3 in the following case. H1: p q,
H2:  (q ʌ r), H3: r, C: p.
8. S.T S  R is tautologically implied by PQ, P→R, Q→S.
9. S.T. R Λ (P V Q) is a valid conclusion from the premises P V Q, Q → R, P → M and M.
10. S.T. R→S can be derived from the premises P→ (Q→S), R V P and Q.
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ASSIGNMENT 2:
1. Define set, powerset, cardinality of set, List and explain various operations performed on
sets.
2. (i) For sets P = {a, b, c, d} and Q = {c, d, e, f, g}, find P ∪ Q and P - Q.
(ii). If Set A = {2, 4, 6, 8} and Set B = {1, 3, 5, 7, 9}, find the Cartesian product A × B and B × A.
3. Let R and S be the following relations A = {a, b, c, d} defined by
R = {(a, a), (a, c), (c, b), (c, d), (d, b)} and S = {(b, a), (c, c), (c, d), (d, a)}
Find i) RoS (ii) SoR iii) RoR.
4. Let X = {1,2,3,4,5,6,7} and R = {(x, y)/x − y is divisible by 3} in X. Show that R is an
equivalence relation.
5. Define Hasse diagram. Draw the Hasse diagram representing the partial ordering.
(a,b)/ a divides bon 1,2,3,4,6,8,12.
6. Define Lattice. If D(n) denotes the lattice of all the divisors of the integer n draw the Hasse
diagrams of D(10), D(15), D(32) and D(45).
7. Draw the Hasse diagrams of the following sets under the partial ordering relation "divides"
and indicate those which are totally ordered. {2, 6, 24}, {3, 5, 15}, {1, 2, 3, 6, 12}, {2, 4, 8, 16},
{3, 9, 27, 54}
8. Check whether the posets {(1, 3, 6, 9), D} and {(1, 5, 25, 125), D} are lattices or not. Justify
your claim.
9. Consider the set D50 = {1, 2, 5, 10, 25, 50} and the relation divides be a partial ordering
relation on D50 .Draw the Hasse diagram of D50 with relation divides. Also Determine all
upper bounds of 5 and 10, lower bounds of 5 and 10, LUB of 5 and 10 and GLB of 5 and 10.
10. Let D100 = {1, 2, 4, 5, 10, 20, 25, 50, 100} be the divisions of 100. Draw the Hasse diagram of
(D100, l) where l is the relation "division".
Find (1) glb {10, 20} (II) lub {10, 20} (III) glb {5, 10, 20, 25} (IV) lub {5, 10, 20, 25}.
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