Question

De Morgan's Laws:

~(A /\ B) <=> ~A \/ ~B



~(A \/ B) <=> ~A /\ ~B



Given the statement, rewrite using De Morgan's Laws, noting that ~(~P) should be equivalently written as P.



A \/ ~B is equivalent to?



Using capital letters, parentheses, and no spaces, give the answer that begins with ~(



Copy and Paste the symbols as needed:



∨ ∧ ⇒

Answer 1

Applying De Morgan's Laws to (A ∨ ¬B) yields ¬(¬A ∧ B), satisfying the specified format and maintaining logical equivalence.

De Morgan's Laws provide a set of logical equivalences involving the negation, conjunction, and disjunction of propositions. The two laws are as follows:

1. ¬(A ∧ B) ≡ ¬A ∨ ¬B

2. ¬(A ∨ B) ≡ ¬A ∧ ¬B

Now, let's apply De Morgan's Laws to the given statement A ∨ ¬B:

¬(A ∨ ¬B) ≈ ¬A ∧ ¬(¬B)

Since ¬(¬B) is equivalent to B, we can simplify further:

¬(A ∨ ¬B) ≈ ¬A ∧ B

Therefore, A ∨ ¬B is equivalent to ¬A ∧ B.

Now, let's express this result using the specified format:

¬(¬A ∧ B)

This expression is in the required format and adheres to the rules stated.