IGNOU SOLVED ASSIGNMENTS FOR 1st Semester MCS-013 2014-2015 Discrete Mathematics
Ans: Comming soon. Now follow - How to write Best ASSIGNMENTS / ANSWERS by Yourself
Question 1
a) Make truth table for
i) p→(q ~ r) ( ~p ~ q ) ii) ~p→(~r q ) (~p r)
b) If A = {1, 2, 3, 4, 5,6,7,8, 9} B = {1, 3, 5, 6, 7, 10,12,15}and C = {1, 2,3, 10,12,15, 45,57} Then find (A B) C.
c) Write down suitable mathematical statement that can be represented by the following symbolic properties. i) ( x) ( y) ( z) P ii) ( x) ( y) ( z) P
Question 2
a) What is proof by mathematical induction? Show that for integers greater than zero: 2n >= n+1.
b) Show whether 17 is rational or irrational.
c) Explain concept of function with the help of an example. What is relation ? Explain following types of relation with example: i) Reflexive ii) Symmetric iii) Transitive
Question 3
a) A survey among the players of cricket club, 20 players are pure batsman,10 players are pure bowler, 40 players are all rounder, and 3 players are wicket keeper batsman. Find the following:
i) How many players can either bat or bowl?
ii) How many players can bowl?
iii) How many players can bat?
b) If p and q are statements, show whether the statement [(p→q) q)] → (~p ~q) is a tautology or not.
Question 4
a) Make logic circuit for the following Boolean expressions:
i) (x′ y z) + (x y z)′
ii) ( x' y) (y′ z) (y z′)
iii) (x y) (y z)
b) Explain principle of duality. Find dual of Boolean expression of the output of the following Boolean expression: ( x' y z) (x y′ z) ′ (x y z′)
Question 5
a) Draw a Venn diagram to represent following:
i) (A B) (C~B) ii) (A B) (B C)
b) if f(x) = log x and g(x) = ex , show that (fog)(x) = (gof)(x).
c) Explain inclusion-exclusion principle with example
Question 6
a) What is pigeonhole principle? Explain its application with the help of an example.
b) If f : R R is a function such that f (x) = 3x2 + 5, find whether f is one - one onto or not. Also find the inverse of f.
Question 7
a) Find how many 4 digit numbers are odd?
b) How many different 10 professionals committees can be formed each containing at least 2 Project Delivery Managers, at least 2 Technical Architects and 3 Security Experts from list of 10 Project Delivery Managers 12 Technical Architects and 5 Security Experts?
c) Explain concept of permutation with an example. How it is different from combination, explain with an example?
Question 8
a) What is Demorgan‟s Law for Boolean algebra? Explain its application with example
b) 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
c) Show whether ( p→q) ( q → p ) is a tautology or not using truth table
Ans: Comming soon. Now follow - How to write Best ASSIGNMENTS / ANSWERS by Yourself
Question 1
a) Make truth table for
i) p→(q ~ r) ( ~p ~ q ) ii) ~p→(~r q ) (~p r)
b) If A = {1, 2, 3, 4, 5,6,7,8, 9} B = {1, 3, 5, 6, 7, 10,12,15}and C = {1, 2,3, 10,12,15, 45,57} Then find (A B) C.
c) Write down suitable mathematical statement that can be represented by the following symbolic properties. i) ( x) ( y) ( z) P ii) ( x) ( y) ( z) P
Question 2
a) What is proof by mathematical induction? Show that for integers greater than zero: 2n >= n+1.
b) Show whether 17 is rational or irrational.
c) Explain concept of function with the help of an example. What is relation ? Explain following types of relation with example: i) Reflexive ii) Symmetric iii) Transitive
Question 3
a) A survey among the players of cricket club, 20 players are pure batsman,10 players are pure bowler, 40 players are all rounder, and 3 players are wicket keeper batsman. Find the following:
i) How many players can either bat or bowl?
ii) How many players can bowl?
iii) How many players can bat?
b) If p and q are statements, show whether the statement [(p→q) q)] → (~p ~q) is a tautology or not.
Question 4
a) Make logic circuit for the following Boolean expressions:
i) (x′ y z) + (x y z)′
ii) ( x' y) (y′ z) (y z′)
iii) (x y) (y z)
b) Explain principle of duality. Find dual of Boolean expression of the output of the following Boolean expression: ( x' y z) (x y′ z) ′ (x y z′)
Question 5
a) Draw a Venn diagram to represent following:
i) (A B) (C~B) ii) (A B) (B C)
b) if f(x) = log x and g(x) = ex , show that (fog)(x) = (gof)(x).
c) Explain inclusion-exclusion principle with example
Question 6
a) What is pigeonhole principle? Explain its application with the help of an example.
b) If f : R R is a function such that f (x) = 3x2 + 5, find whether f is one - one onto or not. Also find the inverse of f.
Question 7
a) Find how many 4 digit numbers are odd?
b) How many different 10 professionals committees can be formed each containing at least 2 Project Delivery Managers, at least 2 Technical Architects and 3 Security Experts from list of 10 Project Delivery Managers 12 Technical Architects and 5 Security Experts?
c) Explain concept of permutation with an example. How it is different from combination, explain with an example?
Question 8
a) What is Demorgan‟s Law for Boolean algebra? Explain its application with example
b) 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
c) Show whether ( p→q) ( q → p ) is a tautology or not using truth table
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