I was wondering if anyone can look over my work, and tell me if i am doing everything correctly? link to the pdf file is below.

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- Sep 11th 2011, 10:26 AMmadseasonCan someone please proofread my homework?
I was wondering if anyone can look over my work, and tell me if i am doing everything correctly? link to the pdf file is below.

hw1(2).pdf - File Shared from Box.net - Free Online File Storage - Sep 11th 2011, 12:45 PMemakarovRe: Can someone please proofread my homework?
Problems 1 and 2: I have not checked every cell in the truth table, but the conclusions are correct. In #2, write explicitly the answer to the question whether P ≡ Q.

Problem 3. You need a more precise proof that x > 1 -> x^2 > x. If x > 1, then x - 1 > 0 and x > 0, so x^2 - x = x(x - 1) > 0 as the product of two positive numbers.

Problem 4. Correct, though the formula is unusual. Usually, one has either $\displaystyle \exists x\,(x>1\land\dots)$ or $\displaystyle \forall x\,(x>1\to\dots)$. This is not to say that the original formula cannot occur somewhere.

Problem 5. $\displaystyle (y+1)^2 < y + 1$ can happen when -1 < y < 0. If you choose a different value of x, you'll need a more accurate proof as well. The overall answer is correct.

Problem 6.Quote:

to prove this statement is false, we need to show that for any arbitrary real number y , ∃x(x^2 < y + 1) is false

It may be a good idea to review how to solve quadratic inequalities.