Working with Biconditionals

        We will here introduce and learn how to use certain rules that apply to biconditionals, to 'if and only if' sentences. Entering the official biconditional sign requires three entries- a '‹' followed by a '-', and then followed by a '›'. However the constructor will make a correct entry for you if you enter '‹›'. Any biconditional p ‹-› q is logically equivalent to the conjunction (p -› q) & (q -› p) and to the conjunction (q -› p) & (p -› q). To eliminate a biconditional use the ‹-›E button. You will be given a choice of lines to add. Recall that when you are given a choice you should pick the one that will be most useful to you. Here is an example:

1. 2. 3. 4. 5.

Q ‹-› S (Q -› S) -› R (Q -› S) & (S -› Q) Q -› S R

Premise Premise 1 ‹-›E 3 &E 2,4 -›E

You should now:

Go to Lesson 1

        Any conjunction (p -› q) & (q -› p) is logically equivalent to the biconditional p ‹-› q and to the biconditional q ‹-› p. The ‹-›I rule allows you to make this move. You will be given a choice of biconditionals. Again you choose the one most useful to you. Here is an example:

1. 2. 3. 4. 5. 6.

Q -› S S -› Q (Q ‹-› S) -› R (Q -› S) & (S -› Q) Q ‹-› S R

Premise Premise Premise 1, 2 &I 4. ‹-›I 3, 5 -›E

You should now:

Go to Lesson 2

Next Section- on Double Negations      Biconditional Exercises      Main Menu