Logic: truth tables: watch it solved step by step

A truth table for any formula in p, q, r with ¬ ∧ ∨ → ↔, and whether it is a tautology, a contradiction or an equivalence. Level: University. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: p & (q | r)

1. The formula. A truth table lists every way the letters can be true (T) or false (F) and works out the formula for each one.
2. Read the structure. Connectives bind in this order: ¬ first, then ∧, then ∨, then →, then ↔. Brackets override. The formula is built from these parts, which become the columns:
3. Fill in the table. Work column by column, left to right: each column uses the ones before it.
4. What the last column says. The last column is true in 3 of 8 rows: a contingency (it depends on the letters).

Answer: contingency (true in 3 of 8 rows)

Practise logic: truth tables with problems the Lab marks for you.