Let `P` and `Q` be two statements, each having two possible truth values: true (`T`) or false (`F`). Then there are exactly [16 unique compound statements involving `P` and `Q`][1] with corresponding truth tables of the form (w,x,y,z). We have given symbols to some of these truth tables; for example - We write the statement corresponding to `(T,F,T,T)` as P⇒Q - We write the statement corresponding to `(T,F,F,T)` as P⊽Q - We write the statement corresponding to `(T,F,F,T)` as P⇔Q Note that these compound statements are logically equivalent to other expressions: - The statement `P⇒Q` has the same truth table as `¬P∨Q` - The statement `P⊽Q` has the same truth table as `¬(P∨Q)` - The statement `P⇔Q` has the same truth table as `(P⇒Q)∧(P⇐Q)` Note in each of the examples above, the compound statement is written at first in the form P(?)Q, and then in a more complicated expression. That is, the first expression writes the compound statement as a [binary operation][2] of P and Q. For instance: - The *implication* maps `(P,Q)` to `P⇒Q` - The *logical nor* maps `(P,Q)` to `P⊽Q` - The *biconditional* maps `(P,Q)` to `P⇔Q` Now the binary operation which maps `(P,Q)` to `P` is called the *logical projection onto `P`*, and the binary operation which maps `(P,Q)` to `Q` is called the *logical projection onto `Q`*. **My question is:** What symbol can be used to represent these two logical projections as binary operations? That is, how can we write these two logical projections in the form `P(?)Q` and `P(¿)Q`? Do these two projection operations have recognized symbols? Unfortunately the Wikipedia page for logical projection looks like it has a lot of room for expansion. (Note: `P` and `Q` are essentially "unary operations"; for the purpose of my question we could have considered the other unary operations `¬P` or `¬Q` or even the two nullary operations `⊤` and `⊥`.) **Edit:** After some time, I seem to have found a possible answer: [this page][3] writes the logical projections as `P L Q` and `P R Q`. That is, we could express projection onto `P` as the binary operation`L(P,Q)` and express projection onto `Q` as the binary operation `R(P,Q)`. [1]: http://en.wikipedia.org/wiki/Truth_table [2]: http://en.wikipedia.org/wiki/Truth_table#Binary_operations [3]: http://finitegeometry.org/sc/16/logic.html