I am not sure how to make truth tables and my book nor my teacher are giving me assistance!

Question

(p↔ ~q)→(q→~p)

Answer 1

Hi Andrew,

 

Your truth tables will always start with all of your variables and all possible T/F combinations for them. From there, you find the truth values of the given problem and put it all together.

 

There are a couple of relationships that are helpful for this particular problem:

 

Think of p ↔q as p = q

Think of p→q as ~p or q

 

For example (I hope the formatting works well; "?" indicates where you should complete the table):

 

p|q|~p|~q|p ↔~q|q →~p|(p →~q)↔(q →~p)|

T|T| F | F  |    F    |    T    |           ?              |

T|F| F | T  |    T    |    T    |           T              |

F|T| T | F  |    ?    |    ?     |           ?              |

F|F| T | T  |    ?    |    ?     |           ?              |

 

In the end, if your last column ends up with every combination being true, the problem statement is true!

 

Hope this helps!

 

If you would like additional help in this class, I would be happy to tutor you online! This course can be tough to pick up at first, but I have the tricks that can help you ace this course.

 

Kind regards,

 

Anthony