1) Let A be set. Show that A - = A using the definition of what it means to be an element of a set.

Add a line for each change and line up the equal signs.When done correctly, this proof will have 5 lines.

2) Use mathematical induction to prove that 1 + 2 + 3 + ... + n = n(n+1)/2for all n >=1

Label your steps, A., B., C., D. E. and provideonlythe parts requested in bold text.

A.Write P(n).

B. Basis step:Showthat P(n) works for some n.

C. The inductive step is how that P(k)

P(k+1).

1. Write P(k)in the form "P(k) = ..."
2. You will assume P(k) and show P(k+1) is true.
3. Write P(k+1)in the form "P(k+1) = ..."

D.Write the proof.

1. The first line should build on the inductive hypothesis.
2. The second line should contain only the RHS of the equation.
3. Add additional lines for each algebraic change, lining up the equal signs.
4. The last line should conclude the proof in terms of k.