Question

1. construct a truth table for the given statement and select the final answer column.

\\ (p \
ightarrow \sim q) \vee (\sim q \wedge p) \\

\

$$\begin{array}{|c|c|c|c|c|c|} \\hline p & q & \\sim q & p \ ightarrow \\sim q & \\sim q \\wedge p & (p \ ightarrow \\sim q) \\vee (\\sim q \\wedge p) \\\\ \\hline t & t & & & & \\\\ \\hline t & f & & & & \\\\ \\hline f & t & & & & \\\\ \\hline f & f & & & & \\\\ \\hline \\end{array}$$

a.
f
t
t
t

b.
t
f
f
f

c.
f
f
t
t

d.
t
t
f
t

Explanation:

Evaluate negation of q

Using the Truth Tables knowledge point

$$
LATEXBLOCK0
$$

Evaluate conditional statement

Using the Mathematical Logic knowledge point

$$
LATEXBLOCK1
$$

Evaluate conjunction statement

Using the Mathematical Logic knowledge point

$$
LATEXBLOCK2
$$

Evaluate final disjunction

Using the Truth Tables knowledge point

$$
LATEXBLOCK3
$$

Answer:

• **(A) F

T
T
T (Correct answer)**

• (B) T

F
F
F

• (C) F

F
T
T

• (D) T

T
F
T