Complete the logic table in figure 1 and solve the inequality −12 ext extlessapprox 5x − 2 ext extless 3

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the questions from the image:

1. Complete the logic table in figure 1

Fill the ~q column (negation of q).
Fill the p ^ ~q column (conjunction of p and ~q).
p q ~q p ^ ~q
T T F F
T F T T
F T F F
F F T F

The completed logic table is shown above.

Solve the inequality $-12 \le 5x - 2 < 3$ and represent the solution.
Add 2 to all parts of the inequality to isolate the term with $x$ .
$-12 + 2 \le 5x - 2 + 2 < 3 + 2$ $-10 \le 5x < 5$
Divide all parts of the inequality by 5 to solve for $x$ .
$\frac{-10}{5} \le \frac{5x}{5} < \frac{5}{5}$ $-2 \le x < 1$
The solution to the inequality is $\boxed{-2 \le x < 1}$ .

Complete the logic table in figure 1 and solve the inequality -12 ext extlessapprox 5x - 2 ext extless 3