Hope everything is ok with you guys...
This week we had our midterm, I don't think I went bad in it, but there was a question in the test, if I'm not mistaken question 2, in which we had to negate a mathematical sentence, that for me was very confusing.
And it was not just negating, in that symbolic sentence we had to negate just the predicate.
Something like:
x 
X , y X , 
z X, x X y = z
And in the exercise we had to negate just the predicate. So:
x X y = z
And my problem was, how can I negate a multiplication? In the test I just thought, ok, so it must be the division.
Researching for this post, I remembered a thing, so basic. That the "and" operator is a way of representing multiplication, so basically:
x X y = z = ((x
y) 
z)
Translating the implication by its and/or form we arrive at:
(¬ (x y) 
z)
Negating this sentence by De Morgan's law we arrive at:
¬ ( (x y) ¬ z )
I think that is the negation of the first sentence, I just thought that would be interesting to present something in this form to its derivation. Please, if my calculations, or logic are wrong, comment!
Something like:
x X , y X , z X, x X y = zAnd in the exercise we had to negate just the predicate. So:
x X y = z
And my problem was, how can I negate a multiplication? In the test I just thought, ok, so it must be the division.
Researching for this post, I remembered a thing, so basic. That the "and" operator is a way of representing multiplication, so basically:
x X y = z = ((x
y) z)Translating the implication by its and/or form we arrive at:
(¬ (x
y) z)Negating this sentence by De Morgan's law we arrive at:
¬ ( (x
y) ¬ z )I think that is the negation of the first sentence, I just thought that would be interesting to present something in this form to its derivation. Please, if my calculations, or logic are wrong, comment!
Hello Ruggi,
ReplyDeleteI can see you have done a nice work understanding the problem. A good way to negate x * y = z is to say that x * y ≠ z. Also, if you want to negate an implication, the best way to do it is to say that the antecedent is true and that the consequent is false; i.e the negation of (x ∧ y) ⇒ z could be (x ∧ y) ∧ ˥ z. I hope this helps. By the way, really nice work, keep it up and feel free to comment on my blog: http://ttesttrying.blogspot.com/
All the best,
Christian