DeMorgans Laws Help?

Question

Use De Morgan’s laws to write an equivalent statement for the following sentence:
If we go to San Antonio, then we will go to Sea World or we will not go to Busch Gardens

Ive got this so far to illustrate the given statement
P --> (Q V ~R)

Now I need to find something equivalent to that and put it into english. Any Help?

Answer 1

Remember that a conditional statement's contrapositive is equivalent to the conditional statement itself.

Contraposition states that p --> q is equivalent to
~q --> ~p.

That means if

P --> (Q v ~R), then the contrapositive would be

~(Q v ~R) ---> ~P

The way DeMorgan's law works is

~(A v B) = ~A ^ ~B
~(A ^ B) = ~A v ~B

Applying this to the contrapositive, we have

(~Q ^ ~~R) ---> ~P. By double negation,
(~Q ^ R) ---> ~P

And translating it:

If we won't go to Sea World AND we will go Busch Gardens, then we won't go to San Antonio.

Answer 2

area a) P(AUB) = P(A) + P(B) - P(A?B) 3/4 = a million/3 + a million/2 - P(A?B) P(A?B) = a million/3 + a million/2 - 3/4 = a million/12 area b) right it incredibly is the place you should use DeMorgan's regulation which states that A' U B' = (A?B)' So, P(A'UB') = P((A?B)') = a million - a million/12 = 11/12 be conscious: DeMorgan's regulation additionally states that A'?B' = (AUB)'

Answer 3

true
p-->(q v r')
=p'v(qvr')
=p'vr'vq
=(p^r)'vq