Answer to Question #214876 in Discrete Mathematics for Taj

Question

Q1. Find the truth tables for the following statement forms:
1. p∨ ∼ q
2. p ∨ (q ∧ r )
3. (p ∨ q) ∧ (p ∨ r )

Answer 1

Let us find the truth tables for the following statement forms:

1. $p∨ ∼ q$

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

2. $p ∨ (q ∧ r )$

$\ \begin{array}{||c|c|c||c|c||} \hline \hline p & q & r & q\land r & p\lor ( q\land r) \\ \hline\hline 0 & 0 & 0 & 0 & 0\\ \hline 0 & 0 & 1 & 0 & 0\\ \hline 0 & 1 & 0 & 0 & 0\\ \hline 0 & 1 & 1 & 1 & 1\\ \hline 1 & 0 & 0 & 0 & 1\\ \hline 1 & 0 & 1 & 0 & 1\\ \hline 1 & 1 & 0 & 0 & 1\\ \hline 1 & 1 & 1 & 1 & 1\\ \hline\hline \end{array}$

3. $(p ∨ q) ∧ (p ∨ r )$

$\ \begin{array}{||c|c|c||c|c|c||} \hline \hline p & q & r & p\lor q & p\lor r & (p\lor q)\land(p\lor r) \\ \hline\hline 0 & 0 & 0 & 0 & 0 & 0\\ \hline 0 & 0 & 1 & 0 & 1 & 0\\ \hline 0 & 1 & 0 & 1 & 0 & 0\\ \hline 0 & 1 & 1 & 1 & 1 & 1\\ \hline 1 & 0 & 0 & 1 & 1 & 1\\ \hline 1 & 0 & 1 & 1 & 1 & 1\\ \hline 1 & 1 & 0 & 1 & 1 & 1\\ \hline 1 & 1 & 1 & 1 & 1 & 1\\ \hline\hline \end{array}$