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I've just started reading a discrete math book, and in the beginning the book covers logic.

One concept I'm finding hard to understand is certain conditional propositions.

When the example uses a word problem, I mostly get it.

The statement is "If The Mathematics Department gets an additional $20,000, then it will hire one new teacher.

p is: "The Mathematics Department gets an additional $20,000.

q is :"The Mathematics Department hires one new faculty member.

If p and q are true, I get why it's true.

If p is true and q is false, I get it.

If both are false, I get it.

But, when p is false and q is true, why is the proposition true?

THEN, I don't seem to have trouble with the word problems, but when numbers are used in place of sentences, I cease to get the concept.

For example, if p is 1>2 and q is 4<8, then the proposition is supposed to be true. I am just not seeing the connection. letter p doesn't seem to relate to q.

Even if both statements are true, lets say p:2>0 and q:3<8, just because one is true, it doesn;t say anything about the other. I know both are true, but the statement " If 2>0, then 3<8" doesn't seem to mean anything to me. I can memorize the truth table, but I'd also like to understand why?

I know I'm just thinking about this badly. I'm not even sure if I'm getting my question across. I'll check back later. Maybe someone will provide some clarity. Maybe I'll understand my confusion better, and ask better questions later.

Thanks for your time,

Steve

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# Conditional Propositions

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