MCS013- SOLVED ASSIGNMENT 2016-17 IGNOU MCA 1st SEM

1. (a) What is proposition? Explain whether, x-y >5 is a

proposition or not.

(b) Make truth table for followings.

(i) p→ (~q ⋁ ~ r) ⋀ (~p ⋁ r)

(ii) p→ (r ⋁ q) ⋀ (~p ⋀ ~q)

(c) Draw a Venn diagram to represent followings:

(i) (A B) (B C)

(ii) (A B) (C~A)

(d) Give geometric representation for followings:

(i) R x { 4}; where R is a natural number

(ii) {2, 2) x ( 2, -4)

2. (a) Write down suitable mathematical statement that can be

represented by the following symbolic properties.

(i) ( x) ( y) ( z) P

(ii) ( x) ( y) ( z) P

(b) Write the following statements in the symbolic form.

(i) Some birds can not fly

(ii) Nothing is correct

(c) What is modus ponen and modus tollen? Write one

example of each.

(d) What is relation? Explain equivalence relation with the

help of an example.

3. (a) Make logic circuit for the following Boolean expressions:

(i) (x' y' z) + (xyz)

(b) Find Boolean Expression of Q in the figure given below.

                                     Figure 1: Boolean Circuit

(c) Find Boolean Expression of Q in the figure given below.

                                        Figure 2: Boolean Circuit

4. (a) How many different committees can be formed of 10

professionals, each containing at least 4 Professors, at

least 3 General Managers and 3 Finance Advisors from list

of 10 Professors, 12 General Managers and 5 Finance

Advisors?

(b) There are two mutually exclusive events A and B with

P(A) =0.5 and P(B) = 0.4. Find the probability of

followings:

(i) A does not occur

(ii) Both A and B does not occur

(iii) Either A or B does not occur

(c) What is set? Explain the basic properties of sets.

5. (a) How many words can be formed using letter of

UMBRELLA using each letter at most once?

(i) If each letter must be used,

(ii) If some or all the letters may be omitted.

(b) Show using truth that:

(p  q)  q ⇒ p ⋁ q

(c) Explain whether (p  q)  (q  r) is a tautology or not.

(d) Prove that: 1 + 2 + 3 + . . . + n = ½n(n + 1) using

mathematical induction.

6. (a) How many ways are there to distribute 15 district objects

into 5 distinct boxes with:

(i) At least three empty box.

(ii) No empty box.

(b) Explain principle of multiplication with an example

(d) Out of 30 students in college 15 takes art courses, 8 takes

biology courses and 6 takes chemistry. It is also known

that 3 students take all the three courses. Show that 7 or

more students taken none of the course.

7. (a) Explain principle of duality with example?

(b) What is power set? Write power set of set

A={1,2,3,4,5,6}.

(c) What is a function? Explain domain and range in context

of function with example.

(d) State and prove the Pigeonhole principle. 

(b) Explain circular permutation with the help of an example. 

(c) What is indirect proof? Explain with an example.

(d) What is Boolean algebra?

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