- Consider the expression x + y− x≡ f. Find f.
- Show −=b.
- Show on the number line the effect of multiplying a number by −1.
- Add the fractions +.
- Find a formula for
^{2},^{3}, and^{4}. Based on what you observe for these, give a formula for^{8}. - When is it true that
^{n}= x^{n}+ y^{n}? - Find the error in the following argument. Let x = y = 1. Then xy = y
^{2}and so xy −x^{2}= y^{2}−x^{2}. Therefore, x=. Dividing both sides byyields x = x + y. Now substituting in what these variables equal yields 1 = 1 + 1. - Find the error in the following argument. = x + 1 and so letting x = 2,= 3 . Therefore, 5 = 9.
- Find the error in the following. Let x = 1 and y = 2. Then ==+= 1 +=. Then cross multiplying, yields 2 = 9.
- Find the error in the following argument. Let x = 3 and y = 1. Then 1 = 3 − 2 =
3 −= x − y== 2
^{2}= 4. - Find the error in the following.
Now let x = 2 and y = 2 to obtain

- Show the rational numbers satisfy the field axioms. You may assume the associative, commutative, and distributive laws hold for the integers.

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