Mathematics

Complete equivalences, build formulas under constraints, translate English into symbols, negate ε–δ statements, and test quantified claims on a directed graph. Every answer is checked by truth table or by evaluation.

Shade Venn regions and test set identities, compute products, power sets and preimages, decide the properties of a relation, and build relations and functions to a specification — or show that none exists.

Read Hasse diagrams and order matrices, find maximal and minimal elements, build partial orders to a specification, analyse orders on intervals of the real line, and find Pareto-efficient points.

Test preference relations for completeness and transitivity, find choice sets, and construct utility functions — or show that none exists.

Solve inequalities as unions of intervals, test claims about order and absolute value, find suprema and infima, run the ε-test for a supremum, and see where ℚ and ℝ part ways.