# Mcs 033 Advanced Discrete Mathematics Solved Assignment 1423

**Q3:**

a) What is Boolean algebra? Write uses of Boolean algebra. Explain how you can find dual of a theorem about Boolean algebra. (5 Marks)

=============Solution Start Here===================

**Boolean Algebra:** What allows us to give reply is the concept of Boolean algebras.

It is possible to design an electric / electronic circuit without actually using switches or logic gates and wires.

As before , let the letters p, q, r......... denote statement or propositions. As you may recall, a tautology T is any proposition witch is always true or always false.

T <= S , F <= S

A Boolean algebra B is an algebraic structure which consists of a set X and two specially defined element 0 or 1 which satisfy the following five laws for all x, y, z belong X.

=============Solution End Here=====================

**b) If p and q are statements, show whether the statement**

** [(p --> q) (~ q)] --> (~ p) is a tautology or not. (5 Marks)**

===========Solution Start Here=======================

p | q | ~p | ~p | ~p ^ ~q | (~p ^ ~q) --> ~p |

T | T | F | F | F | T |

T | F | F | T | F | T |

F | T | T | F | T | T |

F | F | T | T | F | T |

Therefor the statement [(p --> q) ^ (~q)] --> (~p) is a tautology.

===========Solution End Here========================

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IGNOU MCA 3rd Semester Solved Assignments for July-January 2015-16 session is now available here at absolutely free of cost .

We have added MCS-031, MCS-032 and MCS-033, MCS-034, MCS-035 solved assignments and remaining assignments will be added as soon as possible. You can easily download these assignments from below given links and start writing on notebook .

**MCA Third Semester Assignments Details :**

1 – Course Code :MCS-031

Title : Design and Analysis of Algorithms

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2 – Course Code : MCS-032

Title : Object Oriented Analysis and Design

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3 – Course Code : MCS-033

Title : Advanced Discrete Mathematics

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4 – Course Code :MCS-034

Title : Software Engineering

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5 – Course Code : MCS-035

Course Title : Accountancy and Financial Management

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6 – Course Code : MCSL-036

Title : Lab Course

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For July 2015 Session – 31st October, 2015

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