Question

question about proving a tautology without a truth table

Answer 1

I'm stuck on d and e...all of my attempts have been done in this link
http://math.stackexchange.com/questions/644366/verify-a-tautology-without-a-truth-table

it would've been much easier if there was just a p and a q but for d and e there are three letters p q and r . I want to take the left hand side.

Answer 2

@Loser66

Answer 3

:O where did Satellite go?

Answer 4

I prefer @ganeshie8

Answer 5

i gave up on these yesterday itself :(

Answer 6

my second attempt at the problem was to split them up and use double negation .... de morgans but I got some funky stuff in return.

Answer 7

@oldrin.bataku

Answer 8

it requires using the laws, but there are only 2 of them for p q and r unless you're allowed to split them up as A and B

Answer 9

too bad my prof did not give an example

Answer 10

sigh screw this already lol ... XD

Answer 11

my question archive looks bad now with this. I've asked like 5 or 6 times already

Answer 12

http://math.stackexchange.com/questions/644366/verify-a-tautology-without-a-truth-table

it's in there my attempts for d and e @LastDayWork
I'm at my wits end here

Answer 13

yo

Answer 14

So, this is your solution..

Answer 15

yup -.-

Answer 16

Frankly, I don't think it is possible to prove it this way. Can I show my own proof?

Answer 17

sure

Answer 18

First, the notations -
∧ ⇒ AND ⇒ multiplication
∨ ⇒ (inclusive) OR ⇒ Addition
1 ⇒ Tautology
0 ⇒ Fallacy

Boolean algebra can be solved like normal algebra except for the rule
1 + 1 = 1

To apply principle of Duality - http://en.wikipedia.org/wiki/Boolean_algebra#Duality_principle
-Convert every 1 to 0 (and vice-versa)
-Convert every * to + (and vice-versa)
-Leave the variables unchanged

Note: Be careful with the hierarchies. Put * operation in bracket before applying duality to avoid making a mistake.

(d) is obvious.
(e) can be proved using duality and (d); or simply by algebra

Answer 19

I don't know how duality works... though...

Answer 20

the only thing I can think of is using the distributive law on itself. . . . :/

Answer 21

Duality can be proved from the truth table. Its a little laborious though.

Answer 22

too bad I can't use one in this case :/

Answer 23

@UsukiDoll
Hey, it just crossed my mind - if you are having trouble with duality; why don't you use set theory ??

Answer 24

I haven't learned that D:, but I have read it....but that's chapter 2 material :(

Answer 25

Then I am out of options :(

Answer 26

me too aww f it I'll just turn in what I got XD