True or false: If Z ⊃ (R ⊃ F) is true, then ~[Z ⊃ (R ⊃ F)] is false. A statement with the form p ∨ q is false if and only if p is true and q is false. In the statement (S • E) ≡ (X ∨ Y), the triple bar (≡) connects statement E with statement X. A statement with the form p ≡ q is true if and only if p and q are both true. If the conditional (X ∨ M) ⊃ (H ⊃ E) is false, then X ∨ M is true and H ⊃ E is false. A statement with the form p ∨ q is false if and only if p and q are both false. If two statements have opposite truth values, then the disjunction of those statements must be false. If J ⊃ S is true, then J ≡ S must also be true. The horseshoe (⊃) operator expresses a biconditional relation. A truth table is an arrangement of truth values that shows in every possible case how the truth value of a compound proposition is determined by the truth values of its simple components. A statement with the form p ≡ q is true if and only if p and q have identical truth values. The wedge (∨) operator expresses an exclusive, not an inclusive, disjunction. If the conditional (R ∨ F) ⊃ (H ∨ F) is false, then H ∨ F is true and R ∨ F is false.
