Notation Practice and Exit Gate

Attempt without the key. You may look up symbol meanings during practice. For the exit gate, explain the translations without copied notes; ordinary arithmetic checks may follow your prediction.

Practice

1. For g(n) = 3n + 2 on nonnegative integers, evaluate g(0) and g(4). Is -1 in the stated domain?
2. List all valid zero-based indexes for lengths 0 and 4. Explain why the final valid index differs from the length.
3. For S = {1, 3, 5}, decide whether 3 ∈ S, {1, 5} ⊆ S and |S| = 3 are true. Explain why [3, 3] and {3} model different things.
4. Expand Σ(i = 1 to 3) 2i and translate it into a Python loop, showing the excluded stop value.
5. Refute “all positive integers are even” with one counterexample. Explain why three even examples would not prove the claim.

Fresh exit gate

A. For h(n) = 2n + 4 on nonnegative integers, translate the rule, evaluate h(3) and state the permitted inputs.

B. Give valid indexes for an array of length 2, then explain the empty-array case.

C. Expand Σ(j = 2 to 4) j and write an equivalent loop. Explain both endpoints.

D. Explain the difference between “for every file there exists a backup location” and “there exists one backup location for every file.” Give a situation where the first is true but the second is false.

E. Explain why replacing two equal-duration sessions with a set changes the total represented by the history.

Pass when all five translations are correct and independently explained. A missed item routes back to the corresponding section, followed by a changed example. There is no speed requirement or compensation by averaging unrelated answers. Keep the explanations and one code trace as evidence. Recheck one changed translation after a week.

Before Semester 01, also close every outstanding Launchpad algebra task. Neither this notation gate nor calculator fluency replaces the Semester 00 programming and project gates.