Some students attending a small university with a well-known choir live off campus. ████ ███ ████ ████ ███ █████ ██████ ███ ███████ ██ ███ ██████ █ █████████ ██ ███ █████ ██████████ █████████ ████ ████ ██ ███ ████████ ███ ████ ███ ██████ ██ █ █████ ██████
A professor at a small university with a well-known choir concluded that none of the students who live off campus is a music major. Why? Because all music majors are members of the school’s choir.
Based on the argument’s premise, we only know that if you’re a music major, you’re a member of the school’s choir. So why does the professor conclude that none of the students who live off campus is a music major?
The professor’s conclusion follows logically if we assume that all students who live off campus aren’t choir members. (Contrapositive: if you’re a choir member, you don’t live off campus).
The professor's conclusion is properly █████ ██ █████ ███ ██ ███ █████████ ██ ████████
None of the ████████ ███ ████ ███ ██████ ██ █ ██████ ██ ███ ██████
None of the ████████ ███ ███ █████ ██████ ███ ██████ ██ ████ ███ ██████
Some of the ████████ ███ ██ ███ ████ ███ ██████ ███ ███ █████ ███████
All students who ████ ██ ██████ ███ █████ ███████
All students who ███ ███████ ██ ███ █████ ███ █████ ███████
