ganeshie8
  • ganeshie8
@DLS
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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DLS
  • DLS
here we are again :P
ganeshie8
  • ganeshie8
\(p → (p ∧ (q → p))\) lets create the table quick
ganeshie8
  • ganeshie8
we're creating the table to write out PDNF okay

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DLS
  • DLS
We can just read the table from there? just include the picture or something.
ganeshie8
  • ganeshie8
|dw:1450028176976:dw|
ganeshie8
  • ganeshie8
For PDNF simply take the rows with T
ganeshie8
  • ganeshie8
Here all rows have T
ganeshie8
  • ganeshie8
|dw:1450028220939:dw|
ganeshie8
  • ganeshie8
therefore the PDNF is p'q' + p'q + pq' + pq
ganeshie8
  • ganeshie8
replace + with OR gate multiplication with AND gate ' with NOT gate
DLS
  • DLS
you mean to say all rows with atleast 1 T ? or the last column ?
ganeshie8
  • ganeshie8
which column represents the given boolean expression ?
DLS
  • DLS
last one
ganeshie8
  • ganeshie8
that is the reason i have asked you to create teh truth table
ganeshie8
  • ganeshie8
so you only look at the last column
ganeshie8
  • ganeshie8
the other columns help you create that last column ok
DLS
  • DLS
can't believe it is this easy :| DNF is more diffficult than this :O atleast we use theorems and all there
DLS
  • DLS
yep
ganeshie8
  • ganeshie8
the other columns are like scratch work
ganeshie8
  • ganeshie8
these are easy once you understand the logic
DLS
  • DLS
and what would be the modification in case of PCNF ?
ganeshie8
  • ganeshie8
for PCNF you consider the rows with F
ganeshie8
  • ganeshie8
are there any rows with F ?
DLS
  • DLS
nope..so null....right
ganeshie8
  • ganeshie8
yes
ganeshie8
  • ganeshie8
the expression always evaluates to True
ganeshie8
  • ganeshie8
it doesn't depend on the logic values of p and q
DLS
  • DLS
yep so its a tautology
ganeshie8
  • ganeshie8
it is like the function : f(p, q) = 1
ganeshie8
  • ganeshie8
Yep
ganeshie8
  • ganeshie8
im not so sure with ur termonilogy.... the boolean algebra i am familiar with comes from digital circuit design
DLS
  • DLS
alright..I've covered alot of things :) all thanks to you :D
ganeshie8
  • ganeshie8
np :) have good sleep tonight so that you will be fresh tomoro
DLS
  • DLS
yep..going to sleep soon :P just have to revise graph theory n good to go. will remember you name before starting the exam :P

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