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JNTU B.Tech II DISCRETE MATHEMATICS Previous Question Paper (February - 2024 - R22)

B.Tech | II | II-I | R22 | February - 2024

Answer PaperPaper Code: 183ARMaximum Marks: 60Time: 3 Hours

Note: This question paper contains two parts A and B.

i) Part- A for 10 marks, ii) Part - B for 50 marks.

Part-A is a compulsory question which consists of ten sub-questions from all units carrying equal marks.

Part-B consists of ten questions (numbered from 2 to 11) carrying 10 marks each. From each unit, there are two questions and the student should answer one of them. Hence, the student should answer five questions from Part-B.

PART - A

110 marks

Write the following statement in symbolic form: “the crop will be destroyed if there is a flood”.

1 marks

Answer

Let p be "there is a flood" and q be "the crop will be destroyed". The symbolic form is p → q.

Write the following statement in symbolic form: All the first year students know C Programming. Manisha is a first year student.

1 marks

Answer

Let F(x) be "x is a first year student" and C(x) be "x knows C Programming". Let m represent Manisha. The statements are: ∀x(F(x) → C(x)) and F(m).

Define power set.

1 marks

Answer

Prove that

A - (A ∩ B) = A - B

1 marks

Answer

State modular lattice.

1 marks

Answer

State monoid homomorphism.

1 marks

Answer

How many ways can we draw a club and a diamond from a pack of cards?

1 marks

Answer

Find the number of non-negative integral solutions to

n₁ + n₂ + n₃ + n₄ = 20

1 marks

Answer

Does there exist an Eulerian graph with an even number of vertices and an odd number of edges.

1 marks

Answer

Show that a simple connected planar graph with 17 edges and 10 vertices cannot be colored with 2-colors.

1 marks

Answer

PART - B

210 marks

Construct truth table for the following

p → (q ∨ r)

5 marks

Answer

Show that

is a valid inference from the premises

(P ∧ Q), (Q → R), R

5 marks

Answer

Obtain PCNF and PDNF for the following formula

{p → (q ∧ r)} ∧ {¬ p → (¬ q ∧ ¬ r)}

10 marks

Answer

410 marks

Show that

A ∩ (B ∪ A) = A ∪ B

(Assuming corrected equivalence form).

5 marks

Answer

A = {1,3,5,7,8,9}, B = {3,5,8}

, then verify that

(A - B) ∪ (B - A) = (A ∪ B) - (A ∩ B)

5 marks

Answer

Let

f(x) = x+2, g(x) = x-2

and

h(x) = 3x

for

x ∈ R

, where R is the set of real numbers. Find

gof, fog, hog, fo(goh), (fog)oh

10 marks

Answer

610 marks

Construct an OR gate using three NAND gates.

5 marks

Answer

Describe a gating network corresponding to the statement

(x . y) + (y . z) + (z . x)

5 marks

Answer

710 marks

Prove that

(P(S), ∪)

is a monoid.

5 marks

Answer

B = D(24)

be a Lattice, then find all the sublattices of

D(24)

. Also, draw the Hasse diagram.

5 marks

Answer

810 marks

Find the 10th term of

(2x + 1/2x)¹²

5 marks

Answer

Show that

C(n, r) = C(n-1, r-1) + C(n-1, r)

5 marks

Answer

910 marks

Determine the co-efficient of

x⁵ y¹⁰ z⁵ w⁵

is the expansion of

(x + y - z - w)²⁰

5 marks

Answer

Prove that

C(n, 0) + C(n, 2) + ... = C(n, 1) + C(n, 3) + ... = 2^n-1

5 marks

Answer

1010 marks

State and prove fundamental theorem of graph theory.

5 marks

Answer

Let T be a tree with α vertices of degree 1 and β other vertices. Show that the sum of the degrees of the vertices of degree greater than 1 is α + 2(β - 1).

5 marks

Answer

1110 marks

Determine the maximum number of edges in a simple graph with n vertices and k components.

5 marks

Answer

State and Prove Euler's theorem for planar graphs.

5 marks

JNTU B.Tech II DISCRETE MATHEMATICS Previous Question Paper (February - 2024 - R22)

PART - A

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PART - B

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