How do you use Venn diagrams to verify De Morgan's Law?

Question

How do you use Venn diagrams to verify De Morgan's Law: (P \/ Q)’ = P’ /\ Q’

Answer 1

draw two intersecting cicles , named P and Q
, P v Q is the union of the two, (PvQ) ' , is the outside .

P' is the outside of P, Q' the outside of Q,

P' and Q' is the intersection of both outsides

Answer 2

hi, in the photo lower than, there are 2 squares, P and Q, that represent 2 instruments in a Venn diagram. I had to fill sq. P with playstation for spacing and sq. Q with Qs. The area they percentage in the middle has both P and Q. Set P is made up of elements a million and a pair of. Set Q is made up of elements 2 and three. area 4 isn't contained in both P or in Q. in the issue above on the left (P V Q) skill some thing in set P or in set Q. this may genuinely be all of elements a million,2, and three in the diagram. yet then (P V Q)' skill no longer in P or Q, meaning each and every thing else except for elements a million, 2, or 3. obviously, all it extremely is left is a aspect 4. So (P V Q)' = area 4. in the issue above on the right P skill all of elements a million and a pair of, so P' isn't P, it extremely is each and every thing else, elements 3 and four. persevering with on the right, Q skill all of elements 2 and three, so Q' isn't Q, it extremely is each and every thing else, elements a million and four. P' / Q' skill each and every thing it extremely is in both no longer P and in no longer Q. on the grounds that no longer P became elements 3 and four and in no way Q became elements a million and four, then the merely area that became in both no longer P and in no longer Q became area 4. So, P' / Q' = area 4. for this reason, on the grounds that (P V Q)' = area 4 and P' / Q' = area 4, then (P V Q)' = P' / Q'. i'm sorry the diagram became so messy. i'm hoping that enables. :-) _________________ |PPPPPPPPPPPPPP|| |PPPPPPPP-a million-PPPP||-------area 4 |PPP.____________.||______ . |PPP.|PQPQPQPQPQ|QQQQ|| |PPP.|PQPQ-2-PQPQ|.QQQQ|| |_P__|PQ_______PQ|.QQQQQ|| ..........|QQQQQQQQQQQQQQ|| ..........|QQQQ--3--QQQQQQQ-|| ..........|QQQQQQQQQQQQQQ|| ..........|QQ_____QQ______QQ||

Answer 3

draw a vein diagram
label as follows
part only P as "a"
part only Q as "c"
part P u Q as "b"
and part of the universal set not with either P nor Q as "d"

so
P u Q = a,b,c
(P u Q)' = d

now

P' = c,d
Q' = a ,d
so P' intersection Q' =d

therefore (P u Q)' = P' intersection Q'
hence proved

Answer 4

http://www.math.hawaii.edu/~hile/math100/setsc.htm
Please give me best answer thanks!