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, ~A /\ B transforms to ¬A∧B, reflecting the logical equivalence.

To express ~A /\ B using De Morgan's Laws, we utilize the provided laws:

1. ¬(A∧B)≡¬A∨¬B

2. ¬(¬P)≡P

Starting with ~A /\ B, we apply the first law:

¬( A∧B)≡¬( A)∨¬B

Using the second law to simplify ¬( A):

A∨¬B

In symbolic form:

¬(A∧B)≡A∨¬B

Now, let's express ~A /\ B using De Morgan's Laws:

¬( A∧B)≡¬(A∨¬B)

Applying the laws in reverse order:

¬A∧B

Therefore, by De Morgan's Laws, ~A /\ B is logically equivalent to ¬A∧B.