IGNOU MCA(1) MCS-013 Discrete Mathematics Solved Assignment 2019-20 |BCA(2) MCS-013

IGNOU MCA(1) MCS-013 Discrete Mathematics Solved Assignment 2019-20 | BCA(2) MCS-013 Solved Assignment 2019-20

There are eight questions in this assignment, which carries 80 marks. Rest 20 marks are for

viva-voce. Answer all the questions. You may use illustrations and diagrams to enhance the

explanations. Please go through the guidelines regarding assignments given in the

Programme Guide for the format of presentation.

MCA(1) MCS-013 Solved Assignment BCA(2) MCS-013 Solved Assignment 2019-20

Q1.

(a) What is proposition? Explain different logical connectives used in proposition with the

help of example. (3 Marks)

(b) Make truth table for followings. (4 Marks)

i) p→(q  r)  p  ~q

ii) p→(~r  ~ q)  (p  r)

(c) Give geometric representation for followings: (3 Marks)

i) R x { 2}

ii) {1, 5) x ( -2, -3)

Q2.

(a) Draw a Venn diagram to represent followings: (3 Marks)

i) ( A  B  C) ~A

ii) (A  B  C)  (B  C)

(b) Write down suitable mathematical statement that can be represented by the following

symbolic properties. (4 Marks)

i) (  x) (  z) (  y) P

ii)  (x) (  y) (  z) P

(c) Show whether √3 is rational or irrational. (3 Marks)

Q3.

(a) Explain inclusion-exclusion principle with example. (2 Marks)

(b) Make logic circuit for the following Boolean expressions: (4 Marks)

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

ii) (x ' yz) (x ' yz ') (xy ' z)

(c) What is a tautology? If P and Q are statements, show whether the statement

(𝑃 → 𝑄) ∨ (𝑄 → 𝑃) is a tautology or not. (4 Marks)

Q4.

(a) How many words can be formed using letter of STUDENT using each letter at most

once?

i) If each letter must be used,

ii) If some or all the letters may be omitted. (2 Marks)

(b) Show that: (2 Marks)

P=>Q and (~P  Q) are equivalent.

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