Identify the appropriate conclusion based on the premises

Premise 1: If a plant gets sunlight, it grows.

Premise 2: This plant did not grow.

Conclusion:

Question

Identify the appropriate conclusion based on the premises Premise 1: No philosophers are mathematicians. Premise 2: All logicians are philosophers. Conclusion:

Option 1: All logicians are mathematicians.

Option 2: No logician is a mathematician

Option 3: Some philosophers are mathematicians

Option 4: All mathematicians are philosophers.

AfterBoards · Accepted Answer

**Premise 1:** No philosophers are mathematicians. **Premise 2:** All logicians are philosophers. Think of three circles: - The "Logicians" circle sits entirely inside the "Philosophers" circle (because all logicians are philosophers). - The "Philosophers" circle has absolutely no overlap with the "Mathematicians" circle (because no philosophers are mathematicians). So if logicians are *inside* the philosophers group, they too have zero overlap with mathematicians. This gives us: **No logician is a mathematician.** This matches **Option 2**. Let's quickly verify the other options: - **Option 1:** Says all logicians *are* mathematicians — the exact opposite of what we just found. - **Option 3:** Says *some* philosophers are mathematicians — directly contradicts Premise 1. - **Option 4:** Says all mathematicians are philosophers — Premise 1 says no philosophers are mathematicians, which also means no mathematicians are philosophers. So this is wrong too. This is a classic **syllogism** — a logical argument where a conclusion is drawn from two premises: All logicians are philosophers → No philosophers are mathematicians → **Therefore, no logicians are mathematicians** → **correct**

Identify the appropriate conclusion based on the premises $$\newline$$ Premise 1: No philosophers are mathematicians. $\newline$ Premise 2: All logicians are philosophers. $\newline$ Conclusion:

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