Slide 1Slide 2Slide 3DeMorgan’s Laws:¬(P ᴧ Q) (¬P ᴠ ¬Q)¬(P ᴠ Q) (¬P ᴧ ¬Q)Notice that the DeMorgan Laws capture an important relationship between the way negation interacts with conjunction and disjunction.But there are also underlying similarities between the universal quantifier and conjunction:∀x Cube(x)ifCube(a) ᴧ Cube(b) ᴧ Cube(c) ᴧ Cube(d) . . ."And also similarity between the existential quantifier and disjunction:"Ǝx Cube(x)ifCube(a) ᴠ Cube(b) ᴠ Cube(c) ᴠ Cube(d) . . .Because of these similarities, we have …DeMorgan Laws for Quantifiers:"¬∀x P(x) Ǝx ¬P(x)¬Ǝx P(x) ∀x ¬P(x)Just as with regular DeMorgan Laws, where you push the negation in (or out) of the phrase and ‘flip’ the connective, so with DeMorgans for Quantifiers you push the negation past the quantifier and ‘flip’ the quantifier
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