Which function does NOT implement the Karnaugh map given below?

A relation R is defined on the set of integers as zRy if f (x + y) is even. Which of the following statements is true?

Let P(S) denote the power set of a set S. Which of the following is always true?

$${{E_1}}$$ and $${{E_2}}$$ are events in a probability space satisfying the following constraints:
$$ \bullet $$ $$\Pr \,\,({E_1}) = \Pr \,({E_2})$$
$$ \bullet $$ $$\Pr \,\,({E_1}\, \cup {E_2}) = 1$$
$$ \bullet $$ $${E_1}$$ & $${E_2}$$ are independent

The value of Pr ($${E_1}$$), the probability of the event $${E_1}$$, is