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Problem 1

How may the following three statements be arranged so that the first two will make it possible to deduce the third? (a) An eagle has feathers, (b) All birds have feathers. (c) An eagle is a bird.

Expert verified
The correct arrangement of the three statements to deduce the third statement is: (b) All birds have feathers, (a) An eagle has feathers, and (c) An eagle is a bird.
See the step by step solution

Step 1: Identify the conclusion

First, let's determine which statement we want to deduce from the other two. In this case, the conclusion is statement (c), "An eagle is a bird."

Step 2: Determine the logical order

Next, we need to figure out the correct logical order that allows us to deduce statement (c) from the first two statements. There are two potential arrangements: 1. (a) -> (b) -> (c) OR 2. (b) -> (a) -> (c) Let's examine each option:

Step 3: Option 1: (a) -> (b) -> (c)

In this arrangement, we have: 1. An eagle has feathers. 2. All birds have feathers. 3. An eagle is a bird. If we base our conclusion on the first two statements, it does not logically follow that an eagle is a bird because having feathers is not unique to birds (according to these statements). This arrangement does not satisfy our requirement, so let's examine the other option.

Step 4: Option 2: (b) -> (a) -> (c)

In this arrangement, we have: 1. All birds have feathers. 2. An eagle has feathers. 3. An eagle is a bird. If we know that all birds have feathers and that an eagle also has feathers, we can logically deduce that an eagle is a bird (keeping in mind that the statements are simplified for the sake of the exercise). Therefore, arranging the statements this way satisfies our requirement and is the correct answer.

Step 3: Provide the final arrangement

Based on our analysis in the previous steps, the correct arrangement of the three statements to deduce the third statement is: 1. All birds have feathers. (Statement b) 2. An eagle has feathers. (Statement a) 3. An eagle is a bird. (Statement c)

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