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<math>F\!</math> is just one example among &mdash; well, now that I think of it &mdash; how many other logical transformations from the same source to the same target universe?  In the light of that question, maybe it would be advisable to contemplate the character of <math>F\!</math> within the fold of its most closely akin transformations.

F is just one example among -- well, now that I think of it --

how many other logical transformations from the same source

to the same target universe?  In the light of that question,

maybe it would be advisable to contemplate the character of

F within the fold of its most closely akin transformations.

Given the alphabets !U! = {u, v} and !X! = {x, y},

Given the alphabets <math>\mathcal{U} = \{ u, v \}</math> and <math>\mathcal{X} = \{ x, y \},</math> along with the corresponding universes of discourse <math>U^\circ</math> and <math>X^\circ = [\mathbb{B}^2],</math> how many logical transformations of the general form <math>G = (G_1, G_2) : U^\circ \to X^\circ</math> are there?

along with the corresponding universes of discourse

U% and X% ~=~ [B^2], how many logical transformations

of the general form G = <G_1, G_2> : U% -> X% are there?

Since G_1 and G_2 can be any propositions of the type B^2 -> B,

Since G_1 and G_2 can be any propositions of the type B^2 -> B,

there are 2^4 = 16 choices for each of the maps G_1 and G_2, and

there are 2^4 = 16 choices for each of the maps G_1 and G_2, and