Use De Morgan’s law for quantified statements and the laws of propositional logic to show the following equivalences:
a) ¬ x(P (x) ¬Q(x)) x(¬P (x) Q(x))∀∧≡∃∨
b) ¬ x(¬P (x) = Q(x)) x(¬P (x) ¬Q(x))∀⇒≡∃∧
c) ¬ x(¬P (x) (Q(x) ¬R(x))) x(P (x) (¬Q(x) R(x)))

A) ¬(¬q) ≡ q

B) ≡ ( эx) (¬p(x) ∧ ¬q(x)

C) ≡ ( зx ) (p(x) ∧ (¬ q(x) ∨ r(x)) )

Step-by-step explanation:

using De Morgan's law for quantified statements and the laws of propositional logic to show the equivalent of the following

from De -Morgan law

¬(A ∨ B ) = ¬ A ∧¬ B

ATTACHED BELOW IS THE COMPLETE SOLUTION

aloha~! my name is zalgo and i am here to you out on this gracious day. in order to compare the ratios easily, it is best that we simplify the question first. so, the cougars would have 6 wins for 5 losses, bobcats make 2 wins for 1 loss. bulldogs and tigers have a ratio where you can't simplify it. so, the team with the lowest rate would be the bobcats.

i hope that this ! : d

"stay and stay proud! " - zalgo