If $U = \{a, b, c, d, e, f\}$ and $A = \{a, b, c\}$,find $(U \cup A^{\prime})$.

If $A$ and $B$ are two sets,then $A \cap (A \cup B)'$ is equal to

Let $A = \{x : x \in R, |x| < 1\}$; $B = \{x : x \in R, |x - 1| \ge 1\}$ and $A \cup B = R - D$,then the set $D$ is

Write down the power set of $C = \{1, \{2\}\}$.

In a certain town,$25\%$ of the families own a phone and $15\%$ own a car; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements:
$(A) \, 5\%$ families own both a car and a phone
$(B) \, 35\%$ families own either a car or a phone
$(C) \, 40,000$ families live in the town
Then,

The domain of the function $f(x) = \frac{1}{1 + e^x}$ is