Statements: All apples are fruits. All fruits are tasty.
Conclusions: 1. All apples are tasty. 2. Some tasty things are apples.
We are given the following statements:
- All apples are fruits.
- All fruits are tasty.
Now, let's analyze the conclusions:
Conclusion 1: All apples are tasty.
From the two given statements, if all apples are fruits and all fruits are tasty, it logically follows that all apples are tasty. Therefore, conclusion 1 follows.
Conclusion 2: Some tasty things are apples.
This conclusion is not necessarily true. The statement "All fruits are tasty" does not imply that some tasty things are apples. It only suggests that apples are included in the broader category of tasty fruits. Therefore, conclusion 2 does not follow.
Thus, the correct answer is option (b).
Consider the following statements followed by two conclusions.
Statements: 1. Some men are great. 2. Some men are wise.
Conclusions: 1. Men are either great or wise. 2. Some men are neither great nor wise. Choose the correct option:
"In order to be a teacher, one must graduate from college. All poets are poor. Some Mathematicians are poets. No college graduate is poor."
Which of the following is true?
Statements: 1. All cakes are ice cream 2. No ice cream is chocolate
Conclusions: 1. Some cakes are chocolate 2. No cake is chocolate Choose the correct option:
A research team is studying the effects of three different fertilizers (X, Y, and Z) on the growth of a specific plant species. They have four experimental plots with different fertilizer combinations: Plot 1: Fertilizer X only
Plot 2: Fertilizer Y only
Plot 3: Fertilizer X and Fertilizer Z only
Plot 4: Fertilizer Y and Fertilizer Z only
After a period of observation, they note the following: \[\begin{array}{rl} \bullet & \text{Plants in plots with Fertilizer X showed significantly increased height compared to a control group (no fertilizer).} \\ \bullet & \text{Plants in plots with Fertilizer Y showed a slightly increased leaf area compared to the control group.} \\ \bullet & \text{Plants in Plot 3 (X and Z) showed no significant difference in height compared to the control group.} \\ \bullet & \text{Plants in Plot 4 (Y and Z) showed significantly increased height compared to the control group.} \\ \end{array}\] Based on these observations, which of the following conclusions is best supported?
A remote island has a unique social structure. Individuals are either "Truth-tellers" (who always speak the truth) or "Tricksters" (who always lie). You encounter three inhabitants: X, Y, and Z.
X says: "Y is a Trickster"
Y says: "Exactly one of us is a Truth-teller."
What can you definitively conclude about Z?