Use Venn diagrams to determine whether the following standar

Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean standpoint, valid from the Aristotelian standpoint, or invalid.

No AIDS victims are people who pose an immediate threat to the lives of others. Some kindergarten children are AIDS victims. Therefore, some kindergarten children are not people who pose an immediate threat to the lives of others.

Solution

Let A represent Aids victims K kinder garten children.

Thus the intersection of kindergarten and aids victims represent(shaded portion) kindergarden children who are aids patients.

Thus AK is a subset of A

When A does not pose immediate threat to the lives of others, AK, being subset of A cannot pose an immediate threat to the lives of others.

Hence valid.