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Solved Assignment MCS-013 Discrete Mathematics Q-3

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)

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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.

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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
There the proposition we a started with is a tautology.

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

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

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