Question

a certain college offers free tutoring for nine subjects. here is the tutoring schedule for each subject. - math is offered on both monday and wednesday. - german is offered on monday but not wednesday. - art, bio, econ, and psych are offered on wednesday but not monday. - chem, english, and stats are offered on neither monday nor wednesday. write each set in the indicated form. (a) roster form: {math, german, art, bio, econ, psych} descriptive form: select (b) descriptive form: the set of subjects not offered for tutoring on monday roster form: (c) roster form: {math, art, bio, econ, psych} descriptive form: select

Explanation:

subjects not on Monday: Art, Bio, Econ, Psych, Chem, English, Stats? Wait no—wait, "not offered for tutoring on Monday" means subjects whose tutoring day does not include Monday.

Math is on Monday (so excluded), German is on Monday (excluded).

Art: Wed only (not Mon) → include
Bio: Wed only → include
Econ: Wed only → include
Psych: Wed only → include
Chem: neither → include (since not on Mon)
English: neither → include
Stats: neither → include

Wait, but let's check the roster form. Wait, the nine subjects: Math, German, Art, Bio, Econ, Psych, Chem, English, Stats.

Subjects on Monday: Math (Mon+Wed), German (Mon only). So subjects NOT on Monday: subjects that are not in {Math, German}. So: Art, Bio, Econ, Psych, Chem, English, Stats. Wait, but let's check the problem statement: "the set of subjects not offered for tutoring on Monday"—so subjects whose tutoring schedule does not have Monday.

Math is offered on Monday (so it is offered on Monday, so excluded from "not offered on Monday").
German is offered on Monday (excluded).
Art: offered on Wednesday (not Monday) → included.
Bio: Wednesday → included.
Econ: Wednesday → included.
Psych: Wednesday → included.
Chem: neither → not offered on Monday → included.
English: neither → included.
Stats: neither → included.

So the subjects not offered on Monday are Art, Bio, Econ, Psych, Chem, English, Stats? Wait, but let's count: 9 total. Monday has 2 (Math, German), so not Monday: 9 - 2 = 7? Wait, Math is on both, so "offered on Monday" includes Math and German. So "not offered on Monday" is all except Math and German. So: Art, Bio, Econ, Psych, Chem, English, Stats. Let's list them: Art, Bio, Econ, Psych, Chem, English, Stats.

Wait, but let's check the given subjects: the tiles are Art, Bio, Chem, Econ, English, German, Math, Psych, Stats. So yes, those seven.

But wait, maybe I made a mistake. Wait, "not offered for tutoring on Monday" means the subject's tutoring day does not include Monday. So:

• Math: includes Monday → offered on Monday → excluded.
• German: includes Monday → excluded.
• Art: only Wednesday → not offered on Monday → included.
• Bio: only Wednesday → included.
• Econ: only Wednesday → included.
• Psych: only Wednesday → included.
• Chem: neither → not offered on Monday → included.
• English: neither → included.
• Stats: neither → included.

So the set is {Art, Bio, Chem, Econ, English, Psych, Stats}? Wait, wait, Psych is on Wednesday (not Monday) → included. Yes. So that's seven subjects.

Wait, but let's check the roster form. The tiles are Art, Bio, Chem, Econ, English, German, Math, Psych, Stats. So the subjects not on Monday: Art, Bio, Chem, Econ, English, Psych, Stats.

So roster form: {Art, Bio, Chem, Econ, English, Psych, Stats}? Wait, but let's check again. Wait, the problem says "the set of subjects not offered for tutoring on Monday"—so subjects that do not have Monday in their schedule.

Math: Mon and Wed → has Monday → offered on Monday → excluded.
German: Mon only → has Monday → excluded.
Art: Wed only → no Monday → included.
Bio: Wed only → included.
Econ: Wed only → included.
Psych: Wed only → included.
Chem: neither → no Monday → included.
English: neither → included.
Stats: neither → included.

Yes, so those seven. So roster form is {Art, Bio, Chem, Econ, English, Psych, Stats}.

Answer:

For part (b), the roster form is $\{ \text{Art}, \text{Bio}, \text{Chem}, \text{Econ}, \text{English}, \text{Psych}, \text{Stats} \}$