LOGIC , For Students

Step 1: Define Propositions

Let’s extract the key statements from your text as propositions:

1. P: The Charter of Rights exists.

2. Q: Police and authorities are restricted from certain actions (e.g., involuntary commitment).

3. R: Mentally ill people are left untreated and homeless.

4. S: Court cases are delayed.

5. T: Criminals go free due to case dismissals.

6. U: Public becomes aware of systemic problems.

7. V: Government may eventually reform courts.

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Step 2: Express Relationships in Logic

Now we turn the narrative into logical implications.

1. Effect on Mental Health System:

   • If the Charter exists, then police/authorities have new restrictions:

     $$P \rightarrow Q$$

   • If authorities are restricted, untreated mentally ill increase:

     $$Q \rightarrow R$$

   • Chain implication:

     $$P \rightarrow Q \rightarrow R$$

2. Effect on Courts:

   • If the Charter exists, then courts must follow rules like “speedy trial”:

     $$P \rightarrow S$$

   • If cases are delayed beyond the allowed time, then some criminals go free:

     $$S \rightarrow T$$

   • Chain implication:

     $$P \rightarrow S \rightarrow T$$

3. Effect on Public Awareness:

   • If criminals go free, then the public notices problems:

     $$T \rightarrow U$$

   • If the public notices, the government may reform:

     $$U \rightarrow V$$

   • Chain implication:

     $$T \rightarrow U \rightarrow V$$

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Step 3: Combined Logic Diagram

We can combine all chains into a single symbolic map:

$$\begin{align*} P &\rightarrow Q \rightarrow R \quad \text{(mental health issues)} \\ P &\rightarrow S \rightarrow T \rightarrow U \rightarrow V \quad \text{(justice system awareness and reform)} \end{align*}$$

• P (Charter exists) leads to both negative outcomes (R, T) and positive outcomes (U, V).

• Shows a mixed consequence system, which is a perfect example of conditional logic and chain reasoning.

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Step 4: Lesson Points for Students

1. Implication Chains:

   • “If A, then B” can chain: $A \rightarrow B \rightarrow C$.

   • Example: Charter → police restrictions → untreated mentally ill.

2. Mixed Consequences:

   • A single action (P) can cause both negative (R, T) and positive (U, V) outcomes.

   • Introduces non-monotonic reasoning, common in real-world logic.

3. Teaching Exercise:

   • Ask students: “What happens if we remove P? Which outcomes disappear?”

   • Introduces counterfactual reasoning: ¬P → ¬Q, ¬S?

4. Logical Mapping:

   • Helps translate complex narratives into clear logical diagrams.

   • Can also be drawn as a flowchart for visual learners.