Why is $\wedge$ a minimum and $\vee$ a maximum? [closed]
How to remember them?
Long ago someone showed me his method. I still use it sometimes.
Read the three corners like this:
Where did this notation come from?
In lattice theory we have join and meet [see: Helena Rasiowa & Roman Sikorski, The Mathematics of Metamathematics (1963), page 34] :
the least upper bound of $a, b \in A$ will be denoted by $a \cup b$ and called the join of elements $a, b$, and the greatest lower bound of $a, b \in A$ will be denoted by $a \cap b$ and called the meet of $a, b$.
The symbols are motivated by the algebra of sets: the symbols $\cap$ and $\cup$ for intersection and union were used by Giuseppe Peano (1858-1932) in 1888 in Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann.
In propositional calculus we have $\lor$ for disjunction, introduced by Russell in manuscripts from 1902-1903 and in 1906 in Russell's paper "The Theory of Implication," in American Journal of Mathematics, vol. 28.
And we have $\land$ for conjunction: first used in 1930 by Arend Heyting in “Die formalen Regeln der intuitionistischen Logik,” Sitzungsberichte der preußischen Akademie der Wissenschaften, phys.-math. Klasse, 1930.
The link is with boolean algebra and its use as interpretation for the propositional calculus:
a Boolean algebra is a non-empty set $A$, together with two binary operations $∧$ and $∨$ (on $A$), a unary operation $'$, and two distinguished elements $0$ and $1$, satisfying the following axioms [...]. There are several possible widely adopted names for the operations $∧, ∨$, and $'$. We shall call them meet, join, and complement (or complementation), respectively. The distinguished elements $0$ and $1$ are called zero and one.
We can then define a binary relation $\le$ in every Boolean algebra; we write $p \le q$ in case $p ∧ q = p$, and we have that:
For each $p$ and $q$, the set $\{ p, q \}$ has the supremum $p ∨ q$ and the infimum $p ∧ q$.