Needhelpp101
  • Needhelpp101
Determine if the argument is valid or invalid. Give a reason to justify answer. If it is cold, then you need a coat. You do not need a coat. ∴ It is not cold.
Mathematics
chestercat
  • chestercat
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kt7779
  • kt7779
invalid
zugzwang
  • zugzwang
It's actually valid.
anonymous
  • anonymous
valid

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kt7779
  • kt7779
oh
zugzwang
  • zugzwang
TYPO lol if p then q not q therefore not p THIS is the valid one, sorry
zugzwang
  • zugzwang
Modus Tollens*
Needhelpp101
  • Needhelpp101
thanks Guys :)
kt7779
  • kt7779
yep
zugzwang
  • zugzwang
okay, first, we start with p --> q and ~q right?
Needhelpp101
  • Needhelpp101
yeah
zugzwang
  • zugzwang
Well, what does it mean if p implies q? It means either p is false, or q is true, right? Because if p is not false, or p is true, it automatically implies q is true.
Needhelpp101
  • Needhelpp101
yeah
zugzwang
  • zugzwang
So p is false or q is true. At least one of these must be true, right?
zugzwang
  • zugzwang
But you also have the assumption q is false (You do not need a coat)
Needhelpp101
  • Needhelpp101
yep
zugzwang
  • zugzwang
p is false OR q is true. At lease one of these statements is true, and it's NOT the second statement, because we assumed q is false. Then it must be the case that the first statement is true (p is false) or (It is not cold)
Needhelpp101
  • Needhelpp101
ty Zug <3
zugzwang
  • zugzwang
anytime

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