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True or False?

Use your knowledge of truth functions and the five propositional logic operators to determine whether each statement is true or false.

1. If two statements have opposite truth values, then the biconditional of those statements must be true.
2. A biconditional statement is true if and only if its two components are both true.
3. Compound statements using the five propositional logic operators are not truth functional.
4. A statement with the form p • q is true if and only if p and q are both true.
5. If the conjunction [(Z ≡ R) ⊃ F] • ~[B ∨ (T ⊃ P)] is false, then (Z ≡ R) ⊃ F must be false and ~[B ∨ (T ⊃ P)] must be false.
6. If B • P is true, then B ∨ P must also be true.
7. If G ≡ F is true, then G • F must also be true.
8. A statement with the form p ⊃ q is false if and only if p is true and q is false.
9. The horseshoe (⊃) operator (material conditional) does not perfectly capture the meaning of all ordinary language conditional statements.
10. Statement variables, which are used to represent statement forms, are lowercase letters (p, q, r, s, and so on).
11. The dot (•) operator is roughly equivalent to the English word "or."
12. In the statement ~(R • S) ∨ (T ⊃ W), the main operator is the tilde (~).
13. If C ⊃ Q is false and ~D • E is true, then the biconditional (C ⊃ Q) ≡ (~D • E) is false.
14. If A ∨ C is false, and S ≡ D is false, then the conditional (A ∨ C) ⊃ (S ≡ D) is true.
15. For any statement p, p and ~p have identical truth values.