~ ( • B v ~(C choose WFF not WFF D ↔ D WFF not WFF (G->G) -> G WFF not WFF Q~S WFF not WFF (A->S) v (~A v K) WFF not WFF ~~~~~~(~WvX) WFF not WFF Cv->W WFF not WFF
Added by Christine P.
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Well formed formulas For each of the following formulas, determine and prove whether it is in WFF, that is, whether it is a well-formed formula. If you think it is in WFF, prove it by providing a construction sequence (and justify each step in the construction sequence). Otherwise, refer to a property that all well formed formulas have, but this one doesn't have (this could be a property shown in class, or one that you identify and prove yourself here by Induction). (a) ((p1 ∨ (p1)) → (p2 ∨ (p2))) (b) (((p3 ∧ (p1))) ∨ (p1 ∧ p2)) (c) ()p1 ∨ (p2)) → ((p1) → (p3))) (d) ((p1 → ((p2) → p1)) → (p2))
Adi S.
Well-formed formulas (wffs) are defined recursively as follows: T is a wff. F is a wff. Any proposition variable is a wff. If X is a wff, then (¬X) is also a wff. If X and Y are wffs, then (X ∧ Y) is also a wff. If X and Y are wffs, then (X ∨ Y) is also a wff. We say that a formula is in De Morgan normal form if it satisfies the following conditions. ("De Morgan normal form" is not standard terminology; I just made it up.) Every negation in the formula is applied to a variable, not to a more complicated subformula. Either the entire formula is T, or the formula does not contain T. Either the entire formula is F, or the formula does not contain F. Prove that for every wff, there is a logically equivalent wff in De Morgan normal form. For example, the well-formed formula (¬((p ∧ q) ∨ ¬r)) ∧ (¬(p ∨ ¬r) ∧ q) is logically equivalent to the following wff in De Morgan normal form: (((¬p ∨ ¬q) ∧ r)) ∧ ((¬p ∧ r) ∧ q)
Sri K.
What is the negation of the statement ∃y (Q(y) ∧ ∀x
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