# SOLUTION: Construct a truth table for (p &#708; q) &#8596;~q

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 Click here to see ALL problems on Geometric formulas Question 626756: Construct a truth table for (p ˄ q) ↔~qAnswer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!```(p ˄ q) <-> ~q Start with this p|q| T|T| T|F| F|T| F|F| The simplest operation that "(p ˄ q) <-> ~q" contains is the "~q", So make that the heading of the next column: p|q|~q| T|T| | T|F| | F|T| | F|F| | Now fill in the column by looking at the column for q, and remer the rule: If q has a T, ~q will have an F, and vice-versa: p|q|~q| T|T| F| T|F| T| F|T| F| F|F| T| The next simplest operation that (p ˄ q) <-> ~q" contains is the "(p ˄ q)", So make that the heading of the next column: p|q|~q|(p ˄ q)| T|T| F| | T|F| T| | F|T| F| | F|F| T| | Now fill in that column by looking at the columns for p and for q, and remembering the rule for p ˄ q: "T ˄ T" gets a T, but anything else gets a F: p|q|~q|(p ˄ q)| T|T| F| T | T|F| T| F | F|T| F| F | F|F| T| F | The next simplest operation that "(p ˄ q) <-> ~q" contains is the only thing left, the WHOLE THING, "(p ˄ q) <-> ~q" p|q|~q|(p ˄ q)|(p ˄ q) <-> ~q T|T| F| T | T|F| T| F | F|T| F| F | F|F| T| F | Now we fill in that final column by looking at the columns for "(p ˄ q)|" and for ~q, and remembering the rule for <=>: T<->T and F<->F gets T and the others get F p|q|~q|(p ˄ q)|(p ˄ q) <-> ~q T|T| F| T | F T|F| T| F | F F|T| F| F | T F|F| T| F | F Edwin```