In Boolean algebra, a monotonic function is one such that for all "a""i" and "b""i" in {0,1}, if "a"1 ≤ "b"1, "a"2 ≤ "b"2, ..., "a""n" ≤ "b""n" (i.e. the Cartesian product {0, 1}"n" is ordered coordinatewise), then f("a"1, ..., "a""n") ≤ f("b"1, ..., "b""n"). In other words, a Boolean function is monotonic if, for every combination of inputs, switching one of the inputs from false to true can only cause the output to switch from false to true and not from true to false. Graphically, this means that an "n"-ary Boolean function is monotonic when its representation as an "n"-cube labelled with truth values has no upward edge from "true" to "false". (This labelled Hasse diagram is the dual of the function's labelled Venn diagram, which is the more common representation for .)