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HW 6 Possible Answers 1) (a) All lawyers are smart. "x if x is a lawyer then x is smart "x (L1x ® S1x) (b) No doctors understand love. – some doctor understands love. – $x x is a doctor and x understands love. – $x (D1x Ù L1x) (c) Some plumbers are rich. $x x is a plumber and x is rich $x (P1x Ù R1x) (d) Not all doctors are smart – all doctors are smart – "x if x is a doctor then x is smart – "x (D1x ® S1x) (e) Some rich doctor loves Jeremy $x x is a rich doctor and x loves Jeremy $x (x is a rich doctor Ù x loves Jeremy) $x (x is rich and x is a doctor Ù L2xj) $x ([R1x Ù D1x] Ù L2xy) (f) Some plumber insults all smart doctors. $x x is a plumber and x insults all smart doctors $x [Px L "y if y is a smart doctor then x insults y] $x [Px L "y [(Sy L Dy) ® Ixy]] (g) No rich doctor insults any smart lawyer – some rich doctor insults some smart lawyer – $x x is a rich doctor and x insults some smart lawyer – $x [(Rx L Dx) L $y y is a smart lawyer whom x insults] – $x [(Rx L Dx) L $y (Sy L Ly L Ixy)] (h) Every rich plumber hates some smart doctor. "x if x is a rich plumber then x hates some smart doctor "x [(Rx L Px) ® $y y is a smart doctor and x hates y] "x [(Rx L Px) ® $y (Sy L Dy L Hxy)] (i) Some rich plumber hates every smart doctor. $x x is a rich plumber and x hates every smart doctor. $x [Rx L Px L "y if y is a smart doctor then x hates y] $x [Rx L Px L "y [(Sy L Dy) ® Hxy]] (j) No smart plumber whom any rich doctor loves hates any fat lawyer who understands love. – some smart plumber whom some rich doctor loves hates some fat lawyer who understands love. – $x x is a smart plumber and some rich doctor loves x and x hates some fat lawyer who understands love – $x [Sx L Px L $y y is a rich doctor who loves x L $z z is a fat lawyer who understands love and x hates z] – $x [Sx L Px L $y (Ry L Dy L y loves x) L $z (Fz L Lz L Uz L Hxz)] – $x [Sx L Px L $y (Ry L Dy L Lyx) L $z (Fz L Lz L Uz L Hxz)]
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