Symbolizing Exercise 3, problems 13-15

Hi Jim,

How do you translate the following words into symbolic propositions?

  1. “A false proposition is not true.”
  1. “It is false that a true proposition is not false.”
  1. “It is true that it is false that a true proposition is not false.”

I am discombobulated.  


I wrote these problems to make students think through truth values without using symbols. For #1, of course a false proposition is not true, so that is a true statement. For #2, it is TRUE that a true proposition is not false. So this is false. #3 is the same as #2 with an “It is true that” in front of it, which does not change the truth value, so it too is false.

One way you could symbolize it is to make a true statement A, and a false statement X. “It is true that” is just left blank, “not”, “it is false that”, or “is not true” gets negated. Then they could be symbolized this way: 

1.  ~X 
2.  ~~~A
3.  ~~~A

For statements written just like this, you can also simply count falses and nots. If there are an even number, the statement is true, if an odd number, the statements is false.


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