Fe-Fo Svstem Undefined Terms: Fe, Fo Undefined Relation: belongs to Axiom 1. The

Question

Fe-Fo Svstem Undefined Terms: Fe, Fo Undefined Relation: belongs to Axiom 1. There exist exactly three distinct Fe's in this system. Axiom 2. Two distinct Fe's belong to exactly one Fo. Axiom 3. Not all Fe's belong to the same Fo. Axiom 4. Any two distinct Fo's contain at least one Fe which belongs to both. Fe-Fo Theorem 1 Two distinct Fo's have exactly one Fe that belongs to both of them Fe-Fo Theorem 2 There are exactly three Fo's. Fe-Fo Theorem Each Fo has exactly two Fe's that belong to it. 3

Explanation / Answer

Proof: Since there are exactly three distinct Fe's (by Axiom 1), we have at least 3 Fo's by Axiom 3, such that each pair of distinct Fe's belongs to one of these Fo.(*)

Assume that there is another 4th (Fo) says Fo4.

Then Fo4 and each of the other three Fo's have exactly one Fe by Theorem 1

Hence at least two Fe's belongs to F04 which belongs to one of the 3 Fo's by (*)

It contradicts to Axiom 2. Hence a fourth Fo cannot exist.

Therefore there are exactly three Fo's.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.