Given two statements, verify the conclusions and mark the answerStatements: All Grapes are Bananas. All Bananas are Potatoes.Conclusions:I. Some Potatoes are Bananas. II. Some Grapes are Potatoes
Question
Given two statements, verify the conclusions and mark the answerStatements: All Grapes are Bananas. All Bananas are Potatoes.Conclusions:I. Some Potatoes are Bananas. II. Some Grapes are Potatoes
Solution
Let's analyze the statements and conclusions step by step:
Statements:
- All Grapes are Bananas.
- All Bananas are Potatoes.
Conclusions: I. Some Potatoes are Bananas. II. Some Grapes are Potatoes.
Step 1: Analyze the first statement - "All Grapes are Bananas". This means that every single Grape is also a Banana.
Step 2: Analyze the second statement - "All Bananas are Potatoes". This means that every single Banana is also a Potato.
Step 3: Analyze the first conclusion - "Some Potatoes are Bananas". Given that all Bananas are Potatoes (from statement 2), it is correct to say that some Potatoes are Bananas. So, the first conclusion is true.
Step 4: Analyze the second conclusion - "Some Grapes are Potatoes". Given that all Grapes are Bananas (from statement 1) and all Bananas are Potatoes (from statement 2), it is correct to say that some Grapes are Potatoes. So, the second conclusion is also true.
Therefore, both conclusions I and II are true based on the given statements.
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