One circle for each group
Give each group a circle and let the circles overlap. That picture is a Venn diagram. Every part of it is one kind of item. The part inside Amber and outside Birch holds the Amber items that are not Birch items.
Each statement does one of two things to the picture. All and No rule a part out, so you shade it solid gray, and gray means that part is ruled out: nothing is in it. Some says a part holds something, so you put a dot in it, and a dot means at least one item is there.
Shade before you place a dot. A gray part is ruled out, so it cannot take one.
1Draw one circle for each group.
2Shade gray what All and No rule out.
3Put a dot where Some says an item is.
All Amber are Birch. All Birch are Coral.
Three groups, so three circles. Take the statements one at a time.
The first says all Amber are Birch. Shade gray every part of Amber that sits outside Birch. Two parts are ruled out: Amber on its own, and the part of Amber that is inside Coral but outside Birch.
The second says all Birch are Coral. Shade gray every part of Birch that sits outside Coral. That rules out the last part of Amber that was still open outside Coral.
Now read it. The dotted outline on the second picture is Amber outside Coral, and all of it is gray, so all of it is ruled out. Nothing can be an Amber item without being a Coral item, so all Amber are Coral.
Neither statement says that an Amber item exists. So "Some Amber are Coral" does not follow. An empty Amber circle fits both statements.
A dot that could go either side
The statements here are: all Amber are Birch, and some Coral are Birch.
Shade Amber outside Birch gray first. Then place the dot. The second statement puts an item somewhere that is both Coral and Birch, and nothing says which side of the Amber circle it is on. Neither of those two parts is gray, so neither is ruled out, and the dot goes on the line between them.
A dot on a line settles nothing about the circle it sits on.
Try it
Does "Some Coral are Amber" follow?
- Yes, it follows
- No, it does not follow
Show the answer
No, it does not follow
Right. The dot sits on the Amber circle, so the item may be outside Amber, and nothing in the two statements pushes it in.
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