Use a numbered list of arguments to prove that the following argument is valid.
ID: 3145478 • Letter: U
Question
Use a numbered list of arguments to prove that the following argument is valid. Use equivalence laws and valid arguments.
This was the problem given, exactly formatted like this. Notation is Latex, not entirely sure how to clarify because I don't understand what it's asking.
$ eg a (a wedge b)$
$a$
$ herefore eg b$
^Literally what it says on my hw, word for word. can't clarify much more.
Below is my translation for you. not sure if it even makes sense. I'm assuming this is correct, though if you see a mistake in my translation feel free to point it out,
not a ( a and b)
a therefore not b
Explanation / Answer
The correct translation is
not (a and b)
a
-------------------
b
(That 'a' was stray)
Proof:
1. ~(a ^ b) ^ a
(Conjunction)
2. (~a v ~b) ^ a
(De-Morgan's law)
3. (~a ^ a) v (~b ^ a)
(Distributive property)
4. F v (~b ^ a)
(Property of AND)
5. ~b ^ a
(Property of OR)
6. ~b
(Conjunctive simplification).
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