# Basic Theorems in Boolean Algebra

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weyes57 GHSS,Manali - 600068. 1 LAWS AND THEOREMS OF BOOLEAN ALGEBRA PRESENTED BY V.SUBRAMANIAN, P.G.TEACHER(PHYSICS) GOVERNMENT HIGHER SECONDARY SCHOOL, MANALI , CHENNAI – 600 068, TAMILNADU STATE, INDIA.

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BASIC LAWS COMMUTATIVE LAW A+B = B+A AB = BA ASSOCIATIVE LAW A+(B+C) = (A+B)+C A(BC) = (AB)C DISTRIBUTIVE LAW A(B+C) = AB + AC 2 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (1) A+0 = A Considering an OR Gate , One input is A , which can take two values 0 AND 1 . The other input B is equal to 0 . For an OR Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO A . A B Y 0 0 0 1 0 1 3 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (2) A.0 = 0 Considering an AND Gate , One input is A , which can take two values 0 AND 1 . The other input B is equal to 0 . For an AND Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO 0 . A B Y 0 0 0 1 0 0 4 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (3) A+1 =1 Considering an OR Gate , One input is A , which can take two values 0 AND 1 . The other input B is equal to 1 . For an OR Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO 1 . A B Y 0 1 1 1 1 1 5 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (4) A.1 =A Considering an AND Gate , One input is A , which can take two values 0 AND 1 . The other input B is equal to 1 . For an AND Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO A . A B Y 0 1 0 1 1 1 6 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (5) A+A =A Considering an OR Gate , One input is A , which can take two values 0 AND 1 . The other input B is equal to A . For an OR Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO A . A B=A Y 0 0 0 1 1 1 7 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (6) A.A =A Considering an AND Gate , One input is A , which can take two values 0 AND 1 . The other input B is equal to A . For an AND Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO A A B=A Y 0 0 0 1 1 1 8 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (7) A+Ā =1 Considering an OR Gate , One input is A , which can take two values 0 AND 1 . The other input B is compliment of A . For an OR Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO A . A B=Ā Y 0 0 0 1 1 1 9 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (8) A.Ā =0 Considering an AND Gate , One input is A , which can take two values 0 AND 1 . The other input B is compliment of A . For an AND Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO 0 . A B=Ā Y 0 1 0 1 0 0 10 weyes57 GHSS,Manali - 600068.

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NEW OPERATIONS (9) A = Considering a NOT Gate , One input is A , which can take two values 0 AND 1 . The other input B is double compliment of A . For a NOT Gate, From the truth table shown, THE OUTPUT Y IS ALWAYS IS EQUAL TO A . A Ā 1 0 1 0 1 0 11 weyes57 GHSS,Manali - 600068.

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weyes57 GHSS,Manali - 600068. 12 SPECIAL THEOREM 1

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weyes57 GHSS,Manali - 600068. 13 SPECIAL THEOREM 2

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weyes57 GHSS,Manali - 600068. 14 SPECIAL THEOREM 3

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weyes57 GHSS,Manali - 600068. 15 SPECIAL THEOREM 4

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weyes57 GHSS,Manali - 600068. 16 SPECIAL THEOREM 5

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weyes57 GHSS,Manali - 600068. 17 SPECIAL THEOREM 6

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weyes57 GHSS,Manali - 600068. 18 SPECIAL THEOREM 7

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weyes57 GHSS,Manali - 600068. 19 THE END Kindly visit www.freewebs.com/weyes57