Let's match the compound statements to their symbolic forms:

1. "I do not miss class if and only if I like math and the topic of logic is interesting."

   • This statement implies a bi-conditional relationship between not missing class and both liking math and finding the topic of logic interesting.
   • Symbolic form: r ↔ (p ∧ q)

2. "If it isn't true that I like math and I find the topic of logic interesting, then I miss class."

   • This statement expresses that the negation of "I like math and find the topic of logic interesting" leads to missing class.
   • Symbolic form: ∼(p ∧ q) → ∼r

3. "If the topic of logic is interesting and I do not miss class, then I like math."

   • This statement implies that both the topic of logic being interesting and not missing class lead to liking math.
   • Symbolic form: (q ∧ ∼r) → p

4. "If I miss class, then I don't like math or the topic of logic is not interesting."

   • This is an implication stating that missing class leads to either not liking math or the topic of logic not being interesting.
   • Symbolic form: ∼r → ∼p ∨ ∼q

5. "If I miss class, then it isn't true that I like math and the topic of logic is interesting."

   • This statement suggests that missing class implies the negation of both liking math and the topic of logic being interesting.
   • Symbolic form: ∼r → ∼(p ∧ q)

6. "I do not miss class if and only if the topic of logic is interesting and I like math."

   • This is essentially the reverse of the first statement, expressing a bi-conditional between not missing class and both liking math and the topic being interesting.
   • Symbolic form: ∼r ↔ (p ∧ q)

7. "I like math if and only if the topic of logic is interesting, and I do not miss class."

   • This implies a bi-conditional between liking math and the topic of logic being interesting, along with not missing class.
   • Symbolic form: (p ↔ q) ∧ ∼r

8. "If I miss class, then the topic of logic is not interesting, or I like math."

   • This is an implication where missing class leads to either the topic of logic not being interesting or liking math.
   • Symbolic form: ∼r → ∼q ∨ p

9. "If I like math and the topic of logic is interesting, then I do not miss class."

   • This is an implication where both liking math and the topic of logic being interesting lead to not missing class.
   • Symbolic form: (p ∧ q) → ∼r

10. "I like math, and if the topic of logic is interesting, then I do not miss class."

    • This is a conjunction of liking math and an implication that the topic of logic being interesting leads to not missing class.
    • Symbolic form: p ∧ (q → ∼r)

Summary of matches:

1. r ↔ (p ∧ q)
2. ∼(p ∧ q) → ∼r
3. (q ∧ ∼r) → p
4. ∼r → ∼p ∨ ∼q
5. ∼r → ∼(p ∧ q)
6. ∼r ↔ (p ∧ q)
7. (p ↔ q) ∧ ∼r
8. ∼r → ∼q ∨ p
9. (p ∧ q) → ∼r
10. p ∧ (q → ∼r)

Would you like further explanation on any of these?

Related questions:

1. How do you prove the equivalence of two compound statements?
2. What is the difference between a conjunction and a disjunction in logic?
3. How can you use truth tables to verify logical statements?
4. What is the significance of a bi-conditional (↔) in logic?
5. Can logical implications be rewritten in terms of disjunctions?

Tip:

In logic, always break down complex compound statements into simpler components to better understand the relationships between them. This often makes it easier to translate them into symbolic form.