Answer to Question #295329 in Discrete Mathematics for lene

Question

Construct the truth table of the following proposition.

1. (p∧q)→(p∨q)

2. ~(p→q)

3. (p∨q)∧~p

Answer 1

Let us construct the truth table of the following proposition.

1. $(p∧q)→(p∨q)$

$\begin{array}{||c|c||c|c|c||} \hline\hline p & q & p∧q & p∨q & (p∧q)→(p∨q)\\ \hline\hline 0 & 0 & 0 & 0 & 1\\ \hline 0 & 1 & 0 & 1 & 1\\ \hline 1 & 0 & 0 & 1 & 1\\ \hline 1 & 1 & 1 & 1 & 1\\ \hline\hline \end{array}$

2. $\sim(p→q)$

$\begin{array}{||c|c||c|c|c||} \hline\hline p & q & p→q & \sim(p→q) \\ \hline\hline 0 & 0 & 1 & 0 \\ \hline 0 & 1 & 1 & 0 \\ \hline 1 & 0 & 0 & 1 \\ \hline 1 & 1 & 1 & 0 \\ \hline\hline \end{array}$

3. $(p∨q)∧\sim p$

$\begin{array}{||c|c||c|c|c||} \hline\hline p & q & \sim p & p∨q & (p∨q)∧\sim p\\ \hline\hline 0 & 0 & 1 & 0 & 0\\ \hline 0 & 1 & 1 & 1 & 1\\ \hline 1 & 0 & 0 & 1 & 0\\ \hline 1 & 1 & 0 & 1 & 0\\ \hline\hline \end{array}$