Which of the following is not a wff in sl

Question

~H

~H>~J

~T>V~T

~F>~~F

~~F&~~~F

Answer 1

A wff means that it can be decomposed into its atomic sentences by undoing the validly applied logical connectors (~, ^, v, →), assuming that our atomic sentences are themselves wffs (this has to do with the recursive definition of wffs). For example, "~H" is constructed from applying the logical connector "~" to the atomic sentence H. This means that "~H" is a wff because it is constructed from a wff and a valid use of ~, which is applied to any wff such that ~X is a wff for any wff X.

Now, for your examples, the question is if the logical connectors have been correct applied. Note that besides "~" all the others join two wffs together. For this problem, note that "v" must apply to two wffs X and Y such that "X v Y" is a wff. Looking at the third one, we see that "~T>v~T" is not a wff because "v~T" is not a valid application of the logical connector "v."