GATE Exam > GATE Questions > DeMorgan’s theorem states that ________...
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DeMorgan’s theorem states that _________
- a)(AB)’ = A’ + B’
- b)(A + B)’ = A’ * B
- c)A’ + B’ = A’B’
- d)(AB)’ = A’ + B
Correct answer is option 'A'. Can you explain this answer?
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DeMorgan’s theorem states that _________a)(AB)’ = A’...
DeMorgan's laws are a set of rules that relate the logical operators "not", "and", and "or". These laws provide a way to simplify logical expressions and determine the relationship between negations of logical statements.
DeMorgan's first law states that the negation of a conjunction (logical "and") is equivalent to the disjunction (logical "or") of the negations of the individual statements. In other words:
¬(A ∧ B) = ¬A ∨ ¬B
This means that if the statement "A and B" is false, then either "A" is false or "B" is false (or both).
DeMorgan's second law states that the negation of a disjunction (logical "or") is equivalent to the conjunction (logical "and") of the negations of the individual statements. In other words:
¬(A ∨ B) = ¬A ∧ ¬B
This means that if the statement "A or B" is false, then both "A" and "B" must be false.
These laws can be used to simplify logical expressions by applying the negations to individual statements and converting between conjunctions and disjunctions. They are particularly useful when working with complex logical expressions or when proving logical equivalences.
DeMorgan's first law states that the negation of a conjunction (logical "and") is equivalent to the disjunction (logical "or") of the negations of the individual statements. In other words:
¬(A ∧ B) = ¬A ∨ ¬B
This means that if the statement "A and B" is false, then either "A" is false or "B" is false (or both).
DeMorgan's second law states that the negation of a disjunction (logical "or") is equivalent to the conjunction (logical "and") of the negations of the individual statements. In other words:
¬(A ∨ B) = ¬A ∧ ¬B
This means that if the statement "A or B" is false, then both "A" and "B" must be false.
These laws can be used to simplify logical expressions by applying the negations to individual statements and converting between conjunctions and disjunctions. They are particularly useful when working with complex logical expressions or when proving logical equivalences.
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DeMorgan’s theorem states that _________a)(AB)’ = A’...
The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property.
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DeMorgan’s theorem states that _________a)(AB)’ = A’ + B’b)(A + B)’ = A’ * Bc)A’ + B’ = A’B’d)(AB)’ = A’ + BCorrect answer is option 'A'. Can you explain this answer?
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DeMorgan’s theorem states that _________a)(AB)’ = A’ + B’b)(A + B)’ = A’ * Bc)A’ + B’ = A’B’d)(AB)’ = A’ + BCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about DeMorgan’s theorem states that _________a)(AB)’ = A’ + B’b)(A + B)’ = A’ * Bc)A’ + B’ = A’B’d)(AB)’ = A’ + BCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DeMorgan’s theorem states that _________a)(AB)’ = A’ + B’b)(A + B)’ = A’ * Bc)A’ + B’ = A’B’d)(AB)’ = A’ + BCorrect answer is option 'A'. Can you explain this answer?.
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