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:
We are given the following statements: - Some men are great. - Some men are wise. Now, let's analyze the conclusions:
Conclusion 1: Men are either great or wise.
This conclusion is incorrect because from the given statements, we cannot conclude that all men are either great or wise. The statements only say that some men are great and some men are wise, but they don't cover all possibilities.
Conclusion 2: Some men are neither great nor wise.
This conclusion is also incorrect. The statements do not provide any information about men who are neither great nor wise, so we cannot make this conclusion. Thus, neither conclusion follows, so the correct answer is option (d).
"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?
Statements: All apples are fruits. All fruits are tasty.
Conclusions: 1. All apples are tasty. 2. Some tasty things are apples.
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?