(a){(0,0),(1,1),(2,2),(3,3)}

(b){(0,0),(1,1),(2,0),(2,2),(2,3),(3,2),(3,3)}

Que.2. Determine Posets:-

a)(z,=)

b)(z,>=)

c)(z,<=)

Que.3. Is (s,r) a poset if s is set of ale people in world & (a,b)ER, where a&b are people if :

(i)a is taller than b

(ii)a=b or a is an ancestor of b?

Que.4. Find equals of poset:-

(a)({0,1,2}<=)

(b)(z+,/)

Que.5.find incomparable elements of these posets :-

(p({0,1,2})<=)

Que.6. Consider a Poset ({3,5,9,15,24,45},/) , Find

1.maximal elements

2.minimal elements

3.greatest elements

4.least elements

5.Upper bound of {3,5}

6.Lowr bound of {15,45}

Que.7. What is coveling relation of partial ordering {(a,b)/ac=b} on power set of s,where s={1,2,3}?

Que.1. Draw hasse diagram of when d60 is set of all division of 60?

Que.2. Define lattice?

Que.3. Define isomorphic lattice?

Que.4. Consider Poset (a,1) where a={1,2,3,4,6,9,12,18,36} ordered by divisibility &poset (b,1) where b={2,4,6,8}

(i)draw hasse diagram for both poset.

(ii)Find maximal & minimal element in both.

(iii)Find supremum & infimum of every pair of elements in both posets.

(iv)Are these posets lattices?

Que.5. Show that product of two lattices is a lattices.

Que.6. Let S={1,2,3,...12} be poset under divisibility relations. Draw hasse diagram & find first & last element . Also find upper bound, lower bound for subset {5,7,8}.

Que.1. Draw simplified network of f(x,y,z)=x.y.z+x.y'.z+x'.y'z

Que.2. Express the following:- xy'+xz+xy in CNF as well as DNF;

Que.3. Simplify using K Map.Also draw circuit of simplify expression f(a,b,c,d)= Em (0,1,4,5,6,8,9,12,13,14)

Que. 4. Give CNF of expression (y+z') of three variables x,y,z.

Que.5. Define DNF find DNF for (a.b')+(b.c')+(c.a')

Que.6. For every element a&b in Boolean alzebra show that

(i) (a.b)'= a'+b'

(ii) (a+b)'=a'b'

.

Que.1. Show that (p^(-pvq))v(q^~(p^q))=q

Que.2. Write converse, inverse & contrapositive of following statements:

(i)if teacher is absent, then some students do not complete their homework.

(ii)All students complete their homework if they don not have a test

|Que.3. Show that

(p->(q^r))->(-r->-p) is a tantology.

Que.4. Test the validity of following arguments "If i enjoy studying ,then I will study . I will do my homework or I will not study. I will not do my homework. Therefore I do not enjoy studying."

Que.5. Show that (p->q)^(r->q)=(pvr)->q

(Since fn= fn-1 + fn-2 and f0=0,f1=1)

Que.2. Solve the following uncurrence relation

(i)an+2-6an+2+8an=3n2+2-d.3n

(ii)an+3-3an+2-an=24n+48

Que.3. Solve using generating function:-

(i)an-2an-1-3an-2=0

(ii)ar=2an-1+3

Que.4. Define pigeon hole principle.Find minimum no. of boys in the same minute out of 3000 boys on a day.

Que.5. In MCA class of 40 students ,5 are weak. Determine how many ways we can makes a group of students;

(i)Five good students

(ii)Five students in which exactly 3 are weak.

Que.6. Find complete column:-

un-4un1+3un-2=5n+n