Boolean Logic, Validation and Testing

AND is true only when both inputs are true, OR when at least one is true, and NOT reverses truth value. Build a truth table containing all input combinations, then add intermediate columns for combined expressions. Parentheses make intended grouping explicit. Natural-language or can be ambiguous, so identify whether inclusive OR or another operation is required by the question. Do not skip an input combination because it seems unlikely in the real scenario.

Validation checks whether input follows rules such as range, type, length, presence or format. Verification checks that data has been entered or copied as intended, for example through double entry. A value can pass validation and still be factually wrong. Authentication checks identity claims and is a different purpose again. Choose checks that match the actual field rather than adding a generic range check to every kind of data.

Normal data should follow ordinary allowed paths. Boundary tests exercise the edges, and erroneous data should trigger a defined rejection or handling response. For an inclusive range 1–10, test 1 and 10 as well as values just outside. Record input, purpose, expected result, actual result and any correction. Testing can demonstrate failures and improve confidence, but a small collection of passing tests does not prove correctness for every possible input.

Attempt these problems on paper before opening the worked reasoning. Explain your steps as well as giving a final answer.