Compare this boolean expression ! (32 < t && t < 212) // not liquid with the following one (we moved one of the parentheses). ! (32 < t) && t < 212 // ??? The second expression is equivalent to this simpler one. Draw a number line to see why. t <= 32 // frozen -------|---------------------------|------- t 32 liquid 212 Use a number line to analyze this boolean expression. (1 <= x && x <= 5) && (x != 2 && x != 3) -------|--------|--------|--------------|------- 1 2 3 5 Here is an equivalent, easier to read, expression. (1 <= x && x < 2) || (2 < x && x < 3) || (3 < x && x <= 5)