Your expressions
Use A–E, true, false, not, and, xor, or, ->, <-> and parentheses. Clear Expression 2 to study one expression.
Reversing the arrow creates the converse. Find an assignment where the two expressions disagree.
How expressions are read
This explorer uses classical two-valued propositional logic. Each variable is True or False. or includes the both-True case; xor requires exactly one True operand. A -> B is False only when A=True and B=False. A <-> B is True when their values match.
Precedence, strongest first: not → and → xor → or → implication (->) → biconditional (<->). Implication groups to the right: A -> B -> C means A -> (B -> C). Other binary operators group to the left. The grouped forms below make this convention explicit.
- Words and variables accept either case. Symbols other than the listed arrows and parentheses are not part of this grammar.
- Each expression has at most 512 characters, 128 tokens, 32 nested parentheses and 32 nested operators.
- Only A–E are supported, giving at most 32 complete assignments. Constants alone have one empty assignment.
Complete truth table
No differing rows. The complete table has matching outputs throughout.
Why this row matters
Study the connections
The original lesson connects truth values, material implication, equivalence and valid inference through worked explanations and open transfer prompts.
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