∼(C → Q), how do you state this formal sentence into English
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∼(C → Q), how do you state this formal sentence into English

[From: ] [author: ] [Date: 12-02-03] [Hit: ]
because my book doesnt have the answers for even-numbered problems.My answer:If Taylor is not a college student, then she is not qualified for a high-paying job.-I would translate it as Taylor is a college student and Taylor will not be qualified for a high-paying job.Symbolically, the negation of any implication P -> Q is P and (not Q).......
C: Taylor is a college student.
Q: Taylor will be qualified for a high-paying job.

I can't check my answer, because my book doesn't have the answers for even-numbered problems.

My answer:
"If Taylor is not a college student, then she is not qualified for a high-paying job."

-
I would translate it as "Taylor is a college student and Taylor will not be qualified for a high-paying job."

Symbolically, the negation of any implication "P -> Q" is "P and (not Q)". So if you have English translations of any symbolic statements P, Q, the English translation for "the negation of (P -> Q)" is "[translation of P] and [however you would translate the negation of Q]."

If you want to think in terms of English (not that I recommend it), "P -> Q" is something like "if Taylor is a college student, then Taylor will be qualified for a high paying job." To think about negating it, it helps to imagine yourself in a debate, where your opponent has just said this, and you know that it is false. How would you explain why it is false? If you think for a minute, you see that the only way it can be false, is if it is true that Taylor is a college student but also true that Taylor isn't qualified.

As a piece of general advice I wish I had been given sooner in my own life: it can get very awkward and confusing to think mainly in terms of English, because the standard English use and meaning of "if.. then" is much more varied than the formal meaning of "->" in symbolic logic.

For example, often when we use "if.. then", it is to express or emphasize a causal relationship between things (e.g. "if you hit me, then I will be upset"), whereas symbolic -> does not have this property (e.g. P -> Q can be true simply because of an appropriate relationship between the truth value of P and the truth value of Q, not because the statements themselves actually have anything to do with one another).
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