Math logic problem

M

mathwannabe

Junior Member
Joined
Feb 20, 2012
Messages
122
Hello everybody :D

Long time no see :)

I am doing a course in mathematical logic and I have a problem that I can't seem to figure out.

I need to know how did the presenter of the solution for my problem got from this line:

(p AND q AND NOTr) OR (p AND NOTq)

to this one:

[p AND ((q AND NOTr) OR NOTq]

I can't figure it out, I tried to distribute conjunction over disjunction, but the results are not
sattisfying :(

The problem requires me to prove that a formula is a tautology by using elementary transformations, but the transition from mentioned step 1 to step 2 is giving me trouble.

I am sorry for putting this into beginning algebra, but I couldn't find an appropriate section.
 
mathwannabe said:
Hello everybody :D

Long time no see :)

I am doing a course in mathematical logic and I have a problem that I can't seem to figure out.

I need to know how did the presenter of the solution for my problem got from this line:

(p AND q AND NOTr) OR (p AND NOTq)

to this one:

[p AND ((q AND NOTr) OR NOTq]

I can't figure it out, I tried to distribute conjunction over disjunction, but the results are not
sattisfying :(

The problem requires me to prove that a formula is a tautology by using elementary transformations, but the transition from mentioned step 1 to step 2 is giving me trouble.

I am sorry for putting this into beginning algebra, but I couldn't find an appropriate section.
Click to expand...

"Ands" distribute over "Ors" and vise versa. The P was "factored out". Replace "and" with *, and "or" with +.

P*Q*(~R) + P*( ~Q) = P*(Q*(~R)+(~Q))
 
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