Question

Computer Science:
Please be sure to make sure answer is legible if answer is written. :)

Is the set of total Boolean-valued functions, i.e., those whose range is T or F, countable? Prove your answer.

Answer 1

no, uncountable:

here, there are some examples of  boolean valued functions of one argument with an integer
sets of boolean valued functions of one argument:

lets say, a boolean valued function results a set when compared the input with natural number 1.

again, a set is formed when compared the input with two and so on .. since math(required logics) is infinite there forms an infinite sets.

a set is formed when checking whether the input is even and similarly odd , prime, palindrome or not .

so, the sets formed are inifinte and many of them aren't equal. Therefore set of boolean valued are uncountable: