A truth assignment chooses true or false for every distinct variable in a declared list. For the list p, q, the four assignments are (false, false), (false, true), (true, false), and (true, true). To add a new declared variable r, extend each assignment once with r = false and once with r = true. This gives two extensions for each old assignment, doubling the list from four to eight. A declared variable still gets a value even if it never appears in the formula (logical expression).