Draw a conclusion for the statement if possible.

Question

Which answers are correct and why


If it is Monday, then the library is closed. Today is Tuesday

(1 point)
Responses

The library is closed
The library is closed

The library is not closed
The library is not closed

The library is neither open nor closed.
The library is neither open nor closed.

It is not possible to draw a conclusion.
It is not possible to draw a conclusion.
Question 2
Draw a conclusion for the statement if possible.



If a coin is a quarter, then it is worth 25 cents. If a coin is worth 25 cents, then 4 would make a dollar.

(1 point)
Responses

If I have a coin, then I have a quarter.
If I have a coin, then I have a quarter.

If a coin is a quarter, then 4 would make a dollar.
If a coin is a quarter, then 4 would make a dollar.

If it is worth 25 cents, it is a coin.
If it is worth 25 cents, it is a coin.

It is not possible to draw a conclusion.
It is not possible to draw a conclusion.
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Answer 1

Let's analyze both statements and the provided responses.

Question 1

Statement: If it is Monday, then the library is closed. Today is Tuesday.

From the statement, we know:

• The condition for the library being closed (i.e., "If it is Monday") is not met today (because today is Tuesday).
• There is no information provided about whether the library is open or closed on days other than Monday.

Possible Conclusions:

1. The library is closed - This cannot be concluded because the statement only specifies what happens on Monday.
2. The library is not closed - This cannot be concluded because we do not know if the library is open on Tuesday.
3. The library is neither open nor closed - This doesn't make logical sense, as the library must either be open or closed.
4. It is not possible to draw a conclusion - This option is correct; we cannot infer anything about the library's status based solely on the information provided.

Correct Response: It is not possible to draw a conclusion.

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Question 2

Statements:

1. If a coin is a quarter, then it is worth 25 cents.
2. If a coin is worth 25 cents, then 4 would make a dollar.

From the second statement, we can derive some information:

• We know that if a coin is worth 25 cents (which could be true for a quarter, but also for other coins), four of these coins would indeed make a dollar.

Possible Conclusions:

1. If I have a coin, then I have a quarter - This cannot be concluded because having a coin worth 25 cents does not necessarily mean it is a quarter; it could be another coin worth the same amount (like a 25-cent token).
2. If a coin is a quarter, then 4 would make a dollar - This follows logically from the initial statements since a quarter is worth 25 cents, and 4 quarters would make a dollar.
3. If it is worth 25 cents, it is a coin - This is not necessarily true; something could be worth 25 cents but not be a coin (e.g., a token).
4. It is not possible to draw a conclusion - This would not be accurate since we have drawn some logical conclusions.

Correct Response: If a coin is a quarter, then 4 would make a dollar.

In summary:

• For Question 1: It is not possible to draw a conclusion.
• For Question 2: If a coin is a quarter, then 4 would make a dollar.