"xx2x3" - 1 õppematerjal

Diskreetne matemaatika 1. Kodutöö

10. Leida MDNK-le tuletised muutujate x1, x2, x3 ja x4 järgi. Lihtsustada avaldis DNK-ks loogikaalgebra põhiseoste abil. MDNK: f(x1x2 x3x4) = xx1 xx2 x3 V x1 xx2 xx3 V x2 x4 Muutuja x1 järgi: δ f ( x1x 2x 3 x4) δx1 = (xx2 x3 V x2x4) ⊕ (xx2 xx3 V x2x4) = (xx2 xx3 V x2x4) V (xx2 x3 V x2x4)= = [(x2 V xx3 )(xx2 V xx4)] (xx2 xx3 V x2x4) V (xx2 x3 V x2x4) [(x2 V x3)(xx2 V xx4)] = = (x2xx4 V xx2xx3 V xx3xx4) (xx2 xx3 V x2x4) V (xx2 x3 V x2x4)(x2xx4 V xx2x3 V x3xx4) = = xx2xx3 V xx2xx3xx4 V xx2x3 V xx2x3xx4 = xx2xx3 V xx2x3 = xx2 6 Muutuja x2 järgi: δ f ( x1x 2x 3 x4) δx2 = (x1x3 V x1x3) ⊕ (x4) = (xx4) (xx1x3 V x1xx3) V (x4)= = (xx4) (xx1x3 V x1xx3) V (x4)[(x1 V xx3)(xx1 V x3)] = xx1x3xx4 V x1xx3xx4V x1x3x4 V xx1xx3x4 Muutuja x3 järgi: δ f ( x1x 2x 3 x4) δx3 = (xx1xx2 V x2x4) ⊕ (x1xx2 V x2x4) =