Boolean Functions How many unique boolean functions in two variables are there? Of those unique boolean functions, how many depend on neither input (i.e., are constant)? Of those unique boolean functions, how many depend on only one of the two inputs (i.e., the other input has no eect on the output)? Of those unique boolean functions that depend on both inputs, how many of them are identiable / named in common terms (i.e., and, or, etc.)? Using only and, or, not, can you construct formulae for all unique boolean functions on two inputs?

Play a few rounds of minesweeper, as carefully and as thoughtfully as you can. Try to identify at least dierent three clue congurations that let you reason about whether a square is mined or safe, and identify the logical structure of the inference rule you used.