All A's And One B

Nosotros can depict the Venn diagram representation of the statements as shown:

Syllogism: Venn Diagram Representation of Practice Problem 1

Now we don't know the relation between pizzas and burgers, so there is a possibility that some pizzas might be burgers as well. Recall that this is just a possibility. Considering this possibility, we tin as well draw the Venn diagram every bit:

Syllogism: Another Possible Venn Diagram Representation of Practice Problem 1

At present let'southward see which of the conclusions are correct:

I. All noodles are burgers.

This is a likely decision, that is, there is a possibility that this might be true, but as we can come across in the Venn diagrams, it is not a definite determination. The right conclusion would be "Some noodles are burgers".

II. Some noodles are not pizzas.

As we discussed in the text, this is again a probable decision. The right decision would be "Some pizzas are noodles".

III. Some burgers are pizzas.

Again, this is only a likely conclusion. There is merely a possibility that some burgers might exist pizzas. The correct determination would be " Some burgers may or may non exist pizzas" or " Some pizzas may or may non be burgers" .

4. Some burgers may or may non exist pizzas.

Every bit we have already discussed, this is a definite conclusion.

Therefore, but Four is the correct determination.

Note that instead of drawing divide Venn diagrams, we can represent another possibility in the same diagram as the dotted circumvolve: