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 D42.
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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