More on True and False

This page contains more examples of logical statements and their truth values. Some mathematical notation that is used in this module is also revised.

Some of the examples in this module use the symbols $\gt, \ge, \lt$ and $\le$. each can be replaced by words, but they are used because they are short and easy to write.

  • $\gt$ means "is greater than"
  • $\ge$ means "is greater than or equal to"
  • $\lt$ means "is less than"
  • $\le$ means "is less than or equal to"

Here are some examples of statements and their truth values:

  • $1+2=3$.
    This is correct, it is true. Another way of saying this is that the truth value of $1+2=3$ is true.
  • $1+2=7$.
    This is not correct. It is false.
  • The distance from Sydney to Melbourne is $100$km.
    This has truth value false. (It is more than $700$km from Sydney to Melbourne.)
  • $22\ge 33$ (read $22$ is greater than or equal to $33$).
    This is false.
  • $0\lt 6$.
    This is true.

Here are some more practice questions for you. Find the truth value of each statement (that is, decide whether each is true or false). Click on the "Check Answers" button to see if you are correct.

The sky is always red.
$23\le 100$