Auto Service Contract: Clause Exercise

Start with the fictional packet

The FTC recommends comparing a proposed service contract with the existing warranty, including timing and limitations. This exercise translates that comparison into invented rules; it does not determine actual coverage.

FTC guidance supplies the background. Every identifier, number and rule below is invented. There is no actual vehicle, seller or offer. This is a reading exercise, not a recommendation, legal conclusion or payment calculation.

In this fictional packet, A represents an existing warranty; B represents a proposed service contract. t means months elapsed; o means total odometer miles. P and Q are invented repair categories; R is excluded.

Set the common starting point to t = 0 and o = 43,000. Treat t and o as exact readings, not rounded values. The inequalities include both endpoints. Use the recorded readings directly; no conversion or rounding rule is needed.

Scroll sideways to see every column.

For the base packet, a and b are stipulated true. They stand for every unmodeled prerequisite; no specific real-world procedure is implied. Nothing else is tested. Evaluate A and B independently. A true result means only that this invented test passes. Two true results are not two payments.

Try seven cases

For each row, write A and B, A only, B only, or neither. Record the first failed rule for each false result. Do not replace “and” between requirements with “or.”

Scroll sideways to see every column.

1. For C1 specifically, replace B3 with 0 ≤ o ≤ 36,000. What changes? This mutation need not affect only one row.
2. Return to the base packet. For C1, make B4 unreadable. What can you still conclude?
3. Return to the base packet again. For C1, set b to false. Which result changes?

Check the answer key

Scroll sideways to see every column.

Changed basis: C1 becomes A only: 46,000 is greater than 36,000, although 46,000 − 43,000 is not. The mutation changes C1, C2, C3, C5 and C6. C4 and C7 remain neither. Copying a number without its expression changes the rule.

Unreadable B4: A remains true; B is unknown. Its other rules pass, but the missing predicate could be true or false. None of the four complete classifications is justified. “Unknown” records missing evidence, not a failed test.

False b: C1 becomes A only under this amended packet. B4 fails even though B1–B3 pass. Do not silently substitute the amended result into the base answer key.

There is no A-only result under the base rules. A1 implies B1; A2 lies inside B2; A3 makes o − 43,000 fall between 0 and 5,000, inside B3. With both additional predicates true, every passing A also passes B.

What this exercise establishes

The useful output is a trace: the exact rule, its inputs, and whether the evidence makes it true, false or unknown. A larger upper bound alone does not settle a conjunction. An unreadable requirement does not disappear. Keep the original and amended packets separate so another reader can reproduce your result.

This toy system cannot establish a real entitlement, claim outcome or sensible purchase price. It makes no maintenance rule and supplies no state-specific remedy. Its invented scope is deliberately complete only for this exercise.

For the separate borrowing calculation, see isolate the financed cost.