The solution to the recurrence equation
$$T\left( {{2^k}} \right)$$ $$ = 3T\left( {{2^{k - 1}}} \right) + 1$$,
$$T\left( 1 \right) = 1$$ is:

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 $$a, b, c, d$$ be propositions. Assume that the equivalences $$a \leftrightarrow \left( {b \vee \neg b} \right)$$ and $$b \leftrightarrow c$$ hold. Then the truth value of the formulae $$\left( {a\, \wedge \,b} \right) \to \left( {\left( {a \wedge c} \right) \vee d} \right)$$ is always

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