Answer to Question #345602 in Discrete Mathematics for Sasa

Question

Using a Truth table, determine the value of the compound proposition ((𝑝 ∨ 𝑞) ∧ (￢𝑝 ∨ 𝑟)) → (𝑞 ∨ 𝑟).

Answer 1

First, remember the truth tables for basic logical operations :

Before constructing a truth table for the specified expression, we will define a sequence of logical operations. We will denote by numbers from above operations.

$$\left(\left(p\lor^{(1)} q\right)\land^{(4)}\left(\neg p\lor^{(2)} r\right)\right)\longrightarrow^{(5)}\left(q\lor^{(3)} r\right)$$

Now we can construct a truth table for the specified expression.

Q.E.D.