On equality of propositions After the observation that equality of propositions seems to be underused in mathematical reasoning, I discovered that I myself was perhaps not surprisingly only vaguely familiar with all sorts of equalities. This note which is not deep at all is written to remedy that situation. I shall not repeat that ∧ and ∨ are symmetric, associative and mutually distributive; neither shall I repeat de Morgan's laws. The following expressions (E0.i) are all equal.
With the possible exception of the last two, (the socalled "Laws of Absorption") this is very familiar ground. Also expressions (E1.i) are all equal. In the following, = has the lowest binding power
Also expressions (E2.i) are all equal; since (E2.0) is symmetric, they occur in pairs.
The last two were
absolutely new for me; their discovery in a completely different
context provided the incentive to write this note.


Transcriber: Kevin Hely. Last revised on 