Practice problems with verified solutions
Practice sets with solutions verified by the engine: truth tables, simplification, Karnaugh maps, normal forms, argument validity, De Morgan, translation from English, gates and circuits, and the sets for philosophy courses, ISTQB decision tables and MC/DC.
Each set is eight to twelve problems. The solution of every problem was computed by the engine and, where an expected answer is given in a different form, checked for equivalence with it; a set is published only when every problem is verified and the set has been reviewed. Until then the page says so.
Solutions sit behind a toggle so you can attempt a problem first. A PDF export of each set is planned for teachers who hand out exercises.
If you teach, the sets can be embedded or linked from a course page, and the tools let students check their own answers on expressions you did not anticipate.
- Truth table exercises with answers: 2 variables
Ten formulas over two inputs, A and B. For each one, fill in the four rows of the truth table and list the rows on which the formula is TRUE. - Truth table exercises with answers: 3 variables
Ten formulas over A, B and C, eight rows each: the majority function, parity, a multiplexer, implications with compound parts and the “exactly one” pattern. - Truth table exercises with answers: 4 variables
Ten formulas over A, B, C and D, sixteen rows each. - Boolean simplification exercises with answers: basic
Ten one-step simplifications, one law each: identity, domination, idempotence, complement, absorption and double negation. - Boolean simplification exercises with answers: intermediate
Ten simplifications that take two or three laws: distribution followed by complement and identity, De Morgan followed by double negation, absorption on a compound value, and implication elimination. - Boolean simplification exercises with answers: advanced
Ten simplifications beyond single laws: the consensus theorem and its dual, factoring a common term out of three, an XOR that cancels, and implication chains that collapse to a constant or to one… - Karnaugh map exercises with answers: 2 variables
Ten functions given as minterm lists over A and B, to be read off a two-by-two Karnaugh map. - Karnaugh map exercises with answers: 3 variables
Ten functions over A, B and C as minterm lists, to be grouped on a two-row, four-column Karnaugh map. - Karnaugh map exercises with answers: 4 variables
Ten functions over A, B, C and D as minterm lists, to be grouped on the four-by-four Karnaugh map. - CNF and DNF exercises with answers
Ten conversions to disjunctive or conjunctive normal form: implications, XOR and the biconditional in both forms, a negation pushed inward, distribution in both directions, and a maxterm list written… - Argument validity exercises with answers
Ten arguments, each written as one formula (premises) -> (conclusion). - De Morgan's law exercises with answers
Ten negations to push inward until every NOT sits on a single variable: a negated AND, a negated OR, a three-operand chain, a negated implication, and nested cases with two levels. - English to logic translation exercises with answers
Ten sentences to translate into one formula each: rules with “unless”, “only if”, “neither … nor”, “if and only if”, “not both”, exclusive choices, and necessary and sufficient conditions. - Gate diagrams to Boolean expressions: exercises with answers
Ten small gate networks described in words. For each one, write the Boolean expression the output computes, one subexpression per gate, with a gate that feeds another written inside its parentheses. - Boolean expressions to circuits: exercises with answers
Ten formulas to turn into gate lists: for each, name the gates in evaluation order, with their inputs, so that the last gate's output is the formula, and count the gates. - Tautology, contradiction or contingency: exercises with answers
Ten formulas to classify as tautology, contradiction or contingency: the law of excluded middle and its negation, Peirce's law, the contrapositive against the converse, De Morgan as an equivalence… - Logic exercises for philosophy courses, with answers
Ten exercises in the style of an introductory philosophy course: propositions p, q, r joined by the connectives of propositional logic. - Decision table exercises with answers (ISTQB style)
Ten business rules with three or four conditions, in the style of ISTQB decision-table exercises. - MC/DC exercises with answers
Ten decisions for modified condition/decision coverage. - NAND-only and NOR-only design exercises with answers
Ten functions to rebuild from a single gate type, NAND or NOR, as the prompt says.
Questions
Why are some sets marked as in progress?
A set appears in search only once it has at least eight verified problems and a reviewer has read it. Sets are being written in order of demand: truth tables and simplification first, then Karnaugh maps, then the rest.
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Generated from the Tangibool engine, semantics tangibool-semantics/1, engine 1.0.0, build . Every table, map, simplification and verdict on these pages was computed by the Tangibool engine when the site was built, and every claim was re-checked by the same exact checker the app uses. Limits are stated where they apply. © 2026 Foreranger LTD.