Self-study
Every delegate to the convention is a party member. ████ █████████ ██ ███ ██████████ ███ ██████████ ██████████ ███ ████ ██████████ ████████ ███ ██ ██ ███ ██████████ ██ █ ███████ ██ ███ ███████████ ██ █████
Summary
The stimulus can be diagrammed as follows:
Notable Valid Inferences
Some party members are government officials.
Some party members are speakers at the convention.
Some delegates to the convention are speakers at the convention.
18.
If the statements above are █████ ████ █████ ███ ██ ███ █████████ ██████████ ████ ██ █████
a
Every party member ██ ███ ██████████ ██ █ ████████ ██ ███ ███████████
Could be false. While we know that every delegate is a party member, we do not know whether every party member is a delegate. There might be more party members than delegates! (A) confuses the necessary and sufficient conditions.
b
At least some ████████ ██ ███ ██████████ ███ ███████ █████████ ███ █████ ████████
Could be false. We know that some speakers at the convention are delegates and party members, and those speakers could easily constitute the entire lineup! There could also be other speakers, but there don’t have to be.
c
At least some ████████ ██ ███ ██████████ ███ █████████ ██ ███ ███████████
Must be true. As shown below, by chaining the conditional claims, we see that there is a “some before all” relationship between “delegate” and “speaker”. This yields the valid conclusion that at least some delegates are speakers and vice versa.
d
All speakers at ███ ██████████ ███ ██████████ ██████████
Could be false. While we know that every government official at the convention is a speaker, we do not know whether every speaker is a government official. There might be more speakers than government officials! (D) confuses the necessary and sufficient conditions.
e
Every government official ██ ███ ██████████ ██ █ █████ ███████
Could be false. We know that some government officials at the convention are party members, because all delegates are party members and some delegates are government officials. Yet it’s possible that there are also government officials at the convention who are not party members.