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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| 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.
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