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1. Consider the problem SAT: Given a Boolean formula in the variables $x_1, x_2, \ldots, x_n$, using $\wedge$, $\vee$, $\overline{\phantom{x}}$, is there an assignment of 1/0 values to the formula that *satisfies* the formula (i.e., makes the formula evaluate to 1? Evaluate the following instance of SAT.
$$
(x_1 \vee x_2 \vee x_3) \wedge (\overline{x_2} \vee \overline{x_3} \vee \overline{x_4}) \wedge (\overline{x_1} \vee x_2 \vee x_4) \wedge (\overline{x_1} \vee \overline{x_3} \vee \overline{x_4})
$$
2. The formula given in Exercise #1 is in "3-conjunctive normal form:" it consists of an `AND` of a list of clauses $C_1 \wedge C_2 \wedge \cdots \wedge C_k$ where each clause is an `OR` of three "literals," i.e., variables $x_i$ or their negations. For the following counting problems, assume that no clauses are repeated, and ignore the ordering of the clauses (and within the clauses). Give your answers as asymptotic estimates.
    a. How many different formulas in 3-conjunctive normal form can be made using $n$ variables $x_1, x_2, \ldots, x_n$? 
    b. Find an upper bound on the length of a formula (counting literals, connectives, and parentheses). 
    
3. Do Exercise 3 on page 416 of [E].
