Prove that a field of a set $A$ has $2^r$ elements if it has finite cardinality. The definition of algebra is given here "https://en.wikipedia.org/wiki/Field_of_sets" My try: I was trying to start from a simple example. Suppose $F:=\{\phi, X, a_1, a_1^c\}\subseteq A$ where $X$ is the total set. N...