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1. Inequality Proof

For some reason I never thought to subtract f(x) from g(x). It is proved! Thank you!
2. Inequality Proof

Homework Statement If f(x) = (x-1)^2 and g(x) = x+1, then g is greater than or equal to f on the set S = {real numbers x : x is between 0 and 3}. Homework Equations g is greater than or equal to f on the set S of real numbers iff for all s in S, g(s) is greater than f(s). The Attempt at a...
3. Probability Question

I'll believe that. Thank you so much for the help!
4. Probability Question

The answer is 3/32, so it looks like your assumptions are correct. Just to clarify, in this case the order does matter, so UWG is different than WGU? How do we arive at the total number of options, since 36 doesn't seem to fit?
5. Probability Question

I was under the impression that WGU/WUG/GUW/etc. was considered a single combination, should I be thinking of each one as unique?
6. Probability Question

Homework Statement A firm sells a car in four colors; blue, white, green, and black. Three successive orders are placed for the automobile. What is the probability that one blue, one white, and one green are ordered? Exactly two of the orders are the same color? Homework Equations...
7. Real Analysis Proof

Thanks for the replies, I think I figured it out a way to do it. Since it is p iff q, and I can prove if p then q, for the if q then p I just proved the contrapositive, if not p then not q. This should be valid, right? Logic is confusing :rolleyes:
8. Real Analysis Proof

Homework Statement I'm trying to show equivalence of two statements: Let f:S-->T be a function, show that f is 1-1 (injective) is equivalent to f(A n B) = f(A) n f(B) for all A,B subsets of S. The Attempt at a Solution I know equivalence means iff, so I started by assuming f is 1-1...