[p ∧ (p ⇒ q)] ⇒ q

Accepted Solution

The expression � ∧ ( � ⇒ � ) ⇒ � p∧(p⇒q)⇒q is an implication (→) statement that consists of logical operators. To understand and simplify it, let's break it down step by step: � ⇒ � p⇒q is the conditional statement "If p, then q." It is true unless p is true and q is false. � ∧ ( � ⇒ � ) p∧(p⇒q) means "p is true, and the conditional statement 'If p, then q' is true." Finally, ⇒ � ⇒q is another conditional statement "If the previous condition is true, then q." So, the overall expression can be understood as follows: "If p is true and 'If p, then q' is true, then q is true." This is essentially a tautology in classical logic, meaning it is always true regardless of the values of p and q. In other words, the expression is logically valid, and the result is always q being true, regardless of whether p is true or false.