Bachelor of Science in Information Technology (BScIT) – Semester 2/Diploma In Information Technology

Semester - IIDiscrete Mathematics– 4 Credits BT0069

(Book ID: B0953)

Assignment Set – 1 (60 Marks)

Answer All Questions 6 X 10 = 60 Marks

1. Find the number of multiples of 7 among the integers from 200 to 500.

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2. How many numbers between 4000 and 6000 can be formed by using the integers 1, 2, 3, 4, 5, 6, 7 and 8 if any integer is not used more than once?

3. Solve an = 2an-1 + 3an-2 + 5n, n 2, given a0 = -2, a1 = 1.

4. Let S = {a, b, c}. Define “” on P(S), the power set of S as set inclusion. Draw the Hasse diagram for the partially ordered set (P(S), ).

5. In a distributive lattice, if an element has a complement, then prove that it is unique.

6. Define the terms: Graph, finite graph, infinite graph, incidence, degree, isolated vertex, pendent vertex, null graph

Spring- 2012 Diploma In Information Technology Semester - II Discrete Mathematics– 4 Credits (Book ID: B0953) Assignment Set – II (60 Marks) Answer All Questions 6 X 10 = 60 Marks 1. If a group G has only three elements, show that it must be abelian

2. “If there was a meeting then catching the bus was difficult. If they arrived on time catching the bus was not difficult. They arrived on time. Therefore there was no meeting”. Show that the statement constitutes a valid argument .

3. Show that P(x) (x)Q(x) x(P(x) Q(x)).

4. Write the Boolean function values for f : A2 → A, where A = {0, 1} with f (x1, x2) = . 2 1 1 x x x

5. Construct the grammar which generates the following language and also specify their types.

i) 1 , 3n m La b n m

ii) 1n n La ba n

iii) 1 , 1n m La ba n m

6. What is DFA ? Explain with example