(6) Let a, b, c, ...., be k logical variables or propositions that assume values true or false (T or F).?

Consider k-variable boolean functions that map to a set {T, F}. How many different k-variable boolean functions that can be defined? Explain your answer. (Hint: Think about a truth table for k variables.)(6) Let a, b, c, ...., be k logical variables or propositions that assume values true or false (T or F).?
It's useful to think of the number of possible inputs you can have for this function. Since there are k variables, and each of the variables can take two values (T or F), there are 2^k possible inputs.





For example, if k = 2, we have the possible inputs:





(F, F)


(F, T)


(T, F)


(T, T)





of which, as expected, there are 2^2 = 4





Creating a function on these inputs means picking one value out of the two possible (T and F again) for each possible input. Since there are 2^k possible inputs, and two ways to chose the value for each one, there are 2^2^k possible ways to chose the values for all of them.





So there are 2^2^k possible functions.(6) Let a, b, c, ...., be k logical variables or propositions that assume values true or false (T or F).?
If a function f:A--%26gt;B, is defined from A to B, and |A| = n, |B|=m, the number of functions is m^n


In your case 2^k