DISTIBUTIVE LATTICE OF o-INTEGER 12, WITH PROBABILITY INTERPRETATIONS

                                     *
                                     |MAX (P=1)
                                     |
                                     |
                                  max* 12 (P=7/8 =1/2+3/4-1/2*3/4) (complemented)
                                    / \     (join reducible to 4-node & 6-node)
                                   /   \
                  (parordering)-> /     \
                                 /       \<--(parordering)
                                /         \         
                               /           \
     (complemented) (P=1/2) 4 *             * 6 (P=3/4=1/4+1/2-1/4*1/2 by INCLUSION-EXCLUSION Principle.)
  (proper join irreducible)   |            /| (comoplemented, join reducible to 2-node & 3-node)
   (improper atom)            |           / |
                              |          /  |
                              |         /   |
(not parordering but simple)->|        /    |
                              |       /     |
                              |      /      | <-- (parordering)
                              |     /       |
                              |    /        |
                              |   /         |
                              |  /          |
                              | /<-(parord.)|
                              |/            |
   (noncomplemented)  (P=1/4) 2 *             * 3 (P=1/2) (complemented)
  (improper join irreducible, \             |   (improper join irreducible,
   proper atom)                \            /     proper atom)
    (meet of 4-node & 6-node)   \          /
                                 \        /
                                  \      /
                                   \    /
                                    \  /
                                     \/
                                   min* 1 (P=1/8=1/4*1/2) (complemented)
                                      |    (meet of 2-node & 3-node)
                                      |
                                      |
                                      *MIN (P=0)
(Note: Complemented atoms are assigned equiprobabilites = equifractions of 1. Noncomplemented atoms in a LINE successively HALVE the value assigned to their Complemented atom. The MAX and MIN of a lattice are ideal or limit points never attained by join or meet operations. Hence, the 0, 1 probabilities are ideal or limit values, never attained by THE INCLUSION-EXCLUSION PRINCIPLE.)