anonymous
  • anonymous
Are the two statements below logically equivalent? Why or why not? (p ∧ ~q) and ~(p ∨ q)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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precal
  • precal
you need to create truth tables and list all possible solutions for p and q
precal
  • precal
http://www.math.csusb.edu/notes/logic/lognot/node1.html
anonymous
  • anonymous
I have a truth table that's completely filled out except for the part with the exact equation, but I'm not sure what to do with it now.

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precal
  • precal
p and not q not (p and q) I think you can distribute the not and get not p or not q but I am not sure, I have not done this in a very long time. All I know is you have to create truth tables. This is the basis of learning how to write proofs down the road when you are doing undergraduate work in mathematics. Hopefully someone will answer that knows.
precal
  • precal
|dw:1333235991166:dw|
precal
  • precal
Ok I checked it According to Math proof demystified by Stan Gibilisco These are called De Morgan's Laws not (x and y) iff not x or not y not(x or y) iff not x and not y It still does not address your question though
precal
  • precal
|dw:1333236246429:dw|
precal
  • precal
|dw:1333236341503:dw|
anonymous
  • anonymous
(p ∧ ~q) and ~(p ∨ q) r stands for result, truth table for p AND NOT q p q r 0 0 0 0 1 0 1 0 1 1 1 0 NOT (p OR q) p q r 0 0 1 0 1 0 1 0 0 1 1 0 So no, they're not equivalent.
precal
  • precal
you should be looking for when both of these are true. It still goes back to your truth tables
Hero
  • Hero
@bluepig148 , your truth statements are not exactly true
anonymous
  • anonymous
Oops, what ones?
Hero
  • Hero
Your truth tables should present only one truth-false value per line. What you have presented are the general possible values for three variables.
anonymous
  • anonymous
There are only 2 variables in my truth table, the final column is what the boolean function returns given the two inputs.
Hero
  • Hero
Yes, you are right. I should have taken a closer look. They are not the same. I think, in this case, it would have been appropriate to list the actual DeMorgan laws
anonymous
  • anonymous
I started writing a response that simplifies the two expressions and compares them, but then I deleted it to respond to you because I thought my approach was wrong. Lol. I'll do a quick version.
anonymous
  • anonymous
DM's law: a AND b = NOT (NOT a OR NOT b) a OR b = NOT (NOT a AND NOT b) Comparing p AND NOT q and NOT (p OR q) Take a look at the first one and match the patterns. a is p and b is NOT q. Plugging it in, it's the same as: NOT (NOT p OR NOT NOT q) NOT (NOT p OR q) It becomes: NOT (NOT p OR q) vs NOT (p OR q) We can remove the NOT's. NOT p OR q vs p OR q Notice how both sides are being OR'd by q. Then there's NOT p vs p, so they're not the same thing.

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