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Chapter 3: Problem 3

Use Euler diagrams to determine whether each argument is valid or invalid. All clocks keep time accurately. All time-measuring devices keep time accurately. Therefore, all clocks are time-measuring devices.

Short Answer

Expert verified
The argument is invalid. While all clocks and all time-measuring devices do keep time accurately, this is not sufficient to conclude that all clocks are time-measuring devices.

Step by step solution

01

Identify the propositions

The argument consists of two premises and a conclusion. The first premise is 'All clocks keep time accurately'. The second premise is 'All time-measuring devices keep time accurately'. The conclusion is 'Therefore, all clocks are time-measuring devices'.
02

Draw the initial Euler diagrams

Draw separate diagrams for each premise. A circle representing 'clocks' is entirely within a larger circle representing 'things that keep time accurately'. A separate diagram has 'time-measuring devices' entirely within 'things that keep time accurately'.
03

Combine the diagrams

Merge the two diagrams from step 2. You will have one circle representing 'clock' and another representing 'time-measuring devices' both entirely within a larger circle representing 'things that keep time accurately'.
04

Analyze the combined diagram

In this setup, you can see that all clocks are things that keep time accurately and all time-measuring devices are things that keep time accurately. However, in this diagram, clocks and time measuring devices are independent sets which doesn't prove that all clocks are time-measuring devices.

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