Of course! I'll break it down step by step and explain the logical equivalence or implication rule in more detail.

The original statement is: (($X$ AND $Y$) IMPLIES ($W$ OR $Z$))
In logical notation, this is written as: ($(X \land Y) \implies (W \lor Z)$)
Now, let's discuss the implication rule in more detail. The implication rule states that a statement of the form $A \implies B$ is equivalent to $\neg A \lor B$. This means that whenever $A$ implies $B$, either $A$ is false, or $B$ is true (or both). This logical equivalence helps us transform statements with implications into simpler forms, often involving negations and disjunctions (OR).

Let's apply this rule to our original statement:

($(X \land Y) \implies (W \lor Z)$) $\equiv$ ($\neg (X \land Y) \lor (W \lor Z)$)
Here's the step-by-step breakdown:

Step 1: We have an implication in our original statement ($(X \land Y) \implies (W \lor Z)$). In this case, $A$ corresponds to $(X \land Y)$, and $B$ corresponds to $(W \lor Z)$.

Step 2: We apply the implication rule to this statement. According to the rule, $A \implies B$ is equivalent to $\neg A \lor B$. So, we replace $(X \land Y) \implies (W \lor Z)$ with $\neg (X \land Y) \lor (W \lor Z)$.

Step 3: The final equivalent statement is ($\neg (X \land Y) \lor (W \lor Z)$). This means that either the statement $(X \land Y)$ is false, or the statement $(W \lor Z)$ is true (or both).

In summary, the logical equivalent of the statement (($X$ AND $Y$) IMPLIES ($W$ OR $Z$)) is ($\neg (X \land Y)$ OR ($W$ OR $Z$)). This was derived using the logical equivalence known as the implication rule, which helps to simplify statements containing implications by transforming them into statements with negations and disjunctions (OR).
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