Invert any boolean condition

27 December, 2025
Time to read: 1 mins
CSmath
Last update: 27 December, 2025
  • The negation of A || B is !A && !B
  • The negation of A && B is !A || !B

See Boolean algebra, “De Morgan’s laws”: https://en.wikipedia.org/wiki/De_Morgan%27s_laws

An example

An example in C++ from the spdlog library, stdout_sinks-inl.h:

  // don't throw to support cases where no console is attached,
  // and let the log method to do nothing if (handle_ == INVALID_HANDLE_VALUE).
  // throw only if non stdout/stderr target is requested (probably regular file and not console).
  if (handle_ == INVALID_HANDLE_VALUE && file != stdout && file != stderr) {
      throw_spdlog_ex("spdlog::stdout_sink_base: _get_osfhandle() failed", errno);
  }

We group the 2nd and 3rd conditions into a new one:

if (handle_ == INVALID_HANDLE_VALUE && (file != stdout && file != stderr)) {

we apply the rule:

if (handle_ != INVALID_HANDLE_VALUE || !(file != stdout && file != stderr)) {

then apply the rule again on the 2nd part to get the inverted condition:

file == stdout || file == stderr

finally, we substitute it above:

if (handle_ != INVALID_HANDLE_VALUE || file == stdout || file == stderr) {

So the opposite of “if file is an invalid file and no console is attached” is “if file is a valid file or a console is attached”:

  # highlight-start
  // throw if handle_ is valid or a console is attached.
  if (handle_ != INVALID_HANDLE_VALUE || file == stdout || file == stderr) {
  # highlight-end
      throw_spdlog_ex("spdlog::stdout_sink_base: _get_osfhandle() failed", errno);
  }

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