Truth Table For Statement

Question

( S ∨ M) ∨ (∼ M ⊃ S)

How would the truth table be for this statement?

Answer 1

Hi Madison! Though this is a complicated expression, we just have to build it up from all the small pieces. The first two columns are S and M . Then S ∨ M , then ~M , then (~M) ⊃ S , then finally the whole expression. Use the basic rules to build up the table column by column. Let me know how it goes!

Follow-up:

Now is definitely the time to review whatever book or materials you're using on truth tables! I'll give a partial recap:

Our basic propositional variables are S and M , and these can take on any combination of truth values. That means S can be either true or false , and M can be either true or false , which yields four separate combinations to be investigated:

S | M

--------

T | T

T | F

F | T

F | F

The truth value of the other expressions are obtained from the values of S and M following the rules for ~ , ⊃ , and ∨ . These are probably printed in your book.

The method is no different from the way we used to make a table of values in algebra:

x | x^2 – 4

---------------

0 | -4

1 | -3

2 | 0

3 | 5

etc. Except that in algebra, there are infinitely many possibilities for x , while in logic, there are only two (true and false).

Good luck!