MEI

Statements, Logic, and Sets Lab

Mathematics for Engineers I · Module 62765 · Chapter 1

Commit to a prediction, rate your confidence, then reveal the rule in a small, concrete case. When the challenges are complete, use the controls to test new values.

How the lab works

  1. Predict. Choose an answer before the stage changes.
  2. Rate your confidence. A sure but wrong answer marks an idea to revisit first.
  3. Reveal. Compare the result and follow its link back to the guide.
  4. Explore. Finish all four challenges to open each experiment’s controls.

1.1 Truth tables: implication and equivalence

Compare truth values row by row. Swapping the sides of an implication changes its meaning; the contrapositive is the form that stays equivalent. The notes do not name the contrapositive; it follows from their truth table, as the guide shows.

After challenges: drag the marker or focus it and use arrow keys.

Choose truth values
Or try your own

Use A, B, C with ¬ ∧ ∨ ⇒ ⇔ ⊕ (or not, and, or, ->, <->, xor) and brackets.

1.1 Quantifiers: domain and counterexample

A quantified claim is evaluated over its stated domain. One counterexample is enough to disprove a universal claim.

After challenges: drag the marker or focus it and use arrow keys.

Explore a finite domain

1.1 Applications: sensor vote and circuits

Three sensors vote with V ⇔ (A ∧ B) ∨ (A ∧ C) ∨ (B ∧ C), and logical rules shrink circuits. Predict when a single faulty sensor changes the result.

After challenges: drag the marker or focus it and use arrow keys.

Set the sensor readings

1.2 Set operations: membership and De Morgan

Set operations can be checked element by element: membership in a union is OR, while membership in an intersection is AND.

After challenges: drag the marker or focus it and use arrow keys.

Explore membership
Or try your own

Use A, B with ∪ ∩ \ and ᶜ (or ', or, and) and brackets.

1.2 Finite sets: subsets, power set and ordered pairs

Tell an element from a subset, build every subset of a small set, and preserve coordinate order in Cartesian products. These structures are easy to confuse when their elements are written compactly.

After challenges: drag the marker or focus it and use arrow keys.

Explore a set

1.2 Intervals: endpoints and complements

A square bracket includes its endpoint and a round one excludes it. Taking a complement or an intersection decides each end separately.

After challenges: drag the marker or focus it and use arrow keys.

Choose the brackets

Your results

Scores are saved in this browser. “Sure, but wrong” highlights confident mistakes to revisit in the guide.

Personal interactive lab based on Mathematics for Engineers I lecture notes, Chapter 1 “Statements, Logic, and Sets” (printed pages 1–10), by Rhoslyn Coles and Cornelia Schneider. Not an official FAU publication; check course details against the current notes. Made by Thanate Amornjiraporn (Focus).