**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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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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