Answer to Question #308449 in Discrete Mathematics for shouty

Question

Show that (p ∧ q) → (p ∨ q) is a tautology. 

Answer 1

Solution

A  tautology is a proposition that is always true.

To show the given proposition is a Tautology, the truth table of the proposition

$(p ∧ q) → (p ∨ q)$ is shown below.

Furthermore,

$(p ∧ q) → (p ∨ q) ≡ ¬(p ∧ q) ∨ (p ∨ q)$

The last column shows that the proposition $(p ∧ q) → (p ∨ q)$ is a Tautology.