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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’...
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’...
De Morgan's laws are a set of logical equivalences in propositional logic that relate the negation of a conjunction (AND) or disjunction (OR) to the negation of its individual components.
The first law, known as De Morgan's law for conjunction, states that the negation of a conjunction is equivalent to the disjunction of the negations of its components. In symbolic form, this can be expressed as:
¬(p ∧ q) ≡ ¬p ∨ ¬q
This means that if we have a statement "p and q" and we want to negate it, we can instead express it as "not p or not q".
The second law, known as De Morgan's law for disjunction, states that the negation of a disjunction is equivalent to the conjunction of the negations of its components. In symbolic form, this can be expressed as:
¬(p ∨ q) ≡ ¬p ∧ ¬q
This means that if we have a statement "p or q" and we want to negate it, we can instead express it as "not p and not q".
De Morgan's laws are useful in simplifying logical expressions and can be applied to any number of variables or statements. They are widely used in computer science, mathematics, and logic to simplify complex logical statements and proofs.
The first law, known as De Morgan's law for conjunction, states that the negation of a conjunction is equivalent to the disjunction of the negations of its components. In symbolic form, this can be expressed as:
¬(p ∧ q) ≡ ¬p ∨ ¬q
This means that if we have a statement "p and q" and we want to negate it, we can instead express it as "not p or not q".
The second law, known as De Morgan's law for disjunction, states that the negation of a disjunction is equivalent to the conjunction of the negations of its components. In symbolic form, this can be expressed as:
¬(p ∨ q) ≡ ¬p ∧ ¬q
This means that if we have a statement "p or q" and we want to negate it, we can instead express it as "not p and not q".
De Morgan's laws are useful in simplifying logical expressions and can be applied to any number of variables or statements. They are widely used in computer science, mathematics, and logic to simplify complex logical statements and proofs.
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