UNIT:3

1)      Let S be any collection of sets. The relation ‘is subset of ‘ is partial ordering of S . Verify.

2)      Let A= {a,b}. Describe all partial order relation on A.

3)      Define POSET and Hasse Diagram.

4)      Let A = { 1,2,3 ,4,6,8,9,12,18,24} be ordered by relation ‘X divides Y’. Draw  the Hasse Diagram.

5)      Consider the subsets {2,3}, {4,6} and {3,6} in the poset ( {1,2,3,4,5,6},/) find upper bounds, Lower bounds, Suprimum and Infimum  for each subset if exits.

6)      Find all sub Lattices of D₂₄ that contains five or more elements.

7)      Show the relation “ less than or equal to “ on the set of integers is a partial order.

8)      Consider the poset A= ({1,2,3,4,6,9,12,18,36},/). Find the greatest lower bound and least upper  bound of the sets {6,18} and {4,6,9}.

9)      Define Isomorphic Lattices with example.

10)  Prove that the power set P of a set  S is a Lattice under the operation ∩ and U.

11)  What is an Ordered set ?.

₁₂₎      Find the complement of each element of D_42.

13)  Using truth table verify De-Morgans Law.

14)  Simplify Boolean function algebraically and write circuit diagram. (AB+C).(B+C)+C

15)  Draw K- Map and simplify :F(A,B,C,D) = ∑ (0,2,6,8,10,12,14,15)

16)  Write the following Boolean expression in an equivalent product of sums canonical    forming  three variables A, B, and C:     (i)AB                                      (ii)AB’+A’B

17)  Simplify the Boolean Expression: (a) C(B+C) (A+B+C)  (b)  A+B(A+B)+A(A’+B)

18)  Draw Circuit diagram and truth table for Ex OR and Ex Nor gate having two input.

19)  Simplify Boolean Function using K-Map

                                                               i.      F(A,B,C,D)= Σ (0,1,2,3,4,5,6,7,8,9,11)

20)  Write the dual of each Boolean equation: (i) (a*1)*(0+a’)=0   (ii) a + a’b = a+b

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