Problem: Write the Sentence with logic symbols

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The text is:

If she had a lot of money, she would have driven to college in a taxi-cab and never be late. She is always late. It means that she doesn't have a lot of money.

I think that the important parts of this text are:

A: She has a lot of money.

B: She drives in a cab.

C: She is never late.

I think that the answer to this question looks like this: $(A \to B)\wedge(B \to C)$

But what about the 3 part – "She is always late, it means that she doesn't have a lot of money."

I would write it like this: $(\neg C \to \neg A)$.

Question: But how to connect them the right way? I need to write whole formula in a single line.

Also I need to check complete logical formula with resolution method, Quine method and reduction method.

I think that for the Quine method I need to solve this formula with A =(0 and 1) and prove that this is a tautology.

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First of all we must state, that "never" is not negation of "always", so we need another phrase:

  • $D$ - she is always late

Because there is nothing said about the reference between driving a cab and being late, then part "she would have driven to college in a taxi-cab and never be late" can be written just by using the conjcution $\wedge$. The particular statements are also connected with the conjcution $\wedge$.

$(A \Rightarrow (B \wedge C))\wedge D \wedge(D \Rightarrow \neg A)\wedge \neg (C\wedge D)$

The last part ( $\neg (C\wedge D)$ ) is the statement, that tells us, that it is not possible being always late and never late at the same time.