Mcs-013 Discrete Mathematics Solved Assignment Of Aiou

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)

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pq~p~p~p ^ ~q(~p ^ ~q) --> ~p
TTFFFT
TFFTFT
FTTFTT
FFTTFT
There the proposition we a started with is a tautology.

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

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Какая разница? - огрызнулся светловолосый. - Позвольте вам сразу кое-что объяснить, - сказал директор. Секунду спустя оба, залившись краской, делали доклад директору Агентства национальной безопасности. - Д-директор, - заикаясь выдавил светловолосый.  - Я - агент Колиандер.

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