Answer: See the attached image below to see the filled out table.
The Venn diagram is included.
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Step-by-step explanation:
The conditional "If I'm in France, then I'm in Europe" is a true statement.
This is simply because all of France itself is entirely inside Europe. Draw a Venn diagram where one large circle represents "Europe" and a smaller circle inside represents "France". See the diagram below.
No part of the smaller circle is outside the larger circle. We consider France a subset of Europe.
If you were to throw a dart to randomly land inside the "France" circle, then you automatically land inside the "Europe" circle.
Since the conditional is true, there aren't any counter-examples to contradict it. If there were counter-examples, then the conditional would be false.
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The general conditional is of the form "If P, then Q"
We have these templates
- Original Conditional: If P, then Q
- Converse: If Q, then P
- Inverse: If not P, then not Q
- Contrapositive: If not Q, then not P
Each of which is based on the original conditional format. But perhaps a swap happened or negation happened, or both.
The converse has us swap the positions of P and Q.
Which means that if the original conditional is "If I'm in France, then I'm in Europe" becomes "If I'm in Europe, then I'm in France" which is false
A counter-example could be that you might be in Germany, Italy, or Switzerland among other European countries that aren't France. Pick whichever your favorite is.
In other words, just because you are in Europe doesn't 100% guarantee you are in France. You could be inside the "Europe" circle but outside the "France" circle of the venn diagram.
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The inverse of "If P, then Q" is "If not P, then not Q"
So the inverse of "If I'm in France, then I'm in Europe" is "If I'm not in France, then I'm not in Europe" which is false
The reasoning is similar as the previous section. You may be in Germany which is certainly not in France, but you are still in Europe. This is one counter-example of many.
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The contrapositive of "if P, then Q" is "if not Q, then not P"
The contrapositive of "If I'm in France, then I'm in Europe" is "If I'm not in Europe, then I'm not in France" which is true
Since you are outside the "Europe" circle, that means you are definitely outside the "France" circle of the Venn diagram. There's no way to be in France and be outside of Europe at the same time.