Test z okruhu 01.02.2 Logika – predikátový počet

Formuli predikátového počtu `phi=(EE x in U) (AA y in V)(EE z in W) (2x+3y^3>5z)` negujte, potom maximální zjednodušení negace formule `phi` je
`not phi hArr (AA x in U) (EE y in V)(AA z in W) (2x+3y^3>=5z)`
`not phi hArr (AA z in W)(EE y in V) (AA x in U) (2x+3y^3<5z)`
`not phi hArr (AA x in U) (EE y in V)(AA z in W) (2x+3y^3<=5z)`
`not phi hArr (AA x in U) (EE y in V)(AA z in W) (2x+3y^3<5z)`
`not phi hArr (AA z in W)(EE y in V) (AA x in U) (2x+3y^3<=5z)`
Formuli predikátového počtu `phi=(EE y in B) (AA x in A) (5x <= 2y-2)` negujte, potom maximální zjednodušení negace formule `phi` je
`not phi hArr (AA x in B)(EE y in A) (5x > 2y-2)`
`not phi hArr (AA y in B)(EE x in A)( 5x > 2y-2)`
`not phi hArr (AA y in B)(EE x in A)( 5x >= 2y-2)`
`not phi hArr (EE x in A) (AA y in B)( 5x >= 2y-2)`
`not phi hArr (EE x in A) (AA y in B)( 5x > 2y-2)`
Formuli predikátového počtu `phi=(AA c in U) (EE a in V)(AA b in W) (a^5+b^2-13c<=2a^2c^2)` negujte, potom maximální zjednodušení negace formule `phi` je
`not phi hArr (EE b in W)(AA a in V)(EE c in U) (a^5+b^2-13c>=2a^2c^2)`
`not phi hArr (EE b in W)(AA a in V)(EE c in U) (a^5+b^2-13c>2a^2c^2)`
`not phi hArr (EE c in U) (AA a in V)(EE b in W) (a^5+b^2-13c<2a^2c^2)`
`not phi hArr (EE c in U) (AA a in V)(EE b in W) (a^5+b^2-13c>=2a^2c^2)`
`not phi hArr (EE c in U) (AA a in V)(EE b in W) (a^5+b^2-13c>2a^2c^2)`
Formuli predikátového počtu `phi=(AA p in P) (EE q in Q)(AA r in R) (p^3-2q^2+3r<=r^2+2)` negujte, potom maximální zjednodušení negace formule `phi` je
`not phi hArr (EE r in R)(AA q in Q) (EE p in P) (p^3-2q^2+3r>r^2+2)`
`not phi hArr (EE p in P)(AA q in Q) (EE r in R) (p^3-2q^2+3r>r^2+2)`
`not phi hArr (EE p in P)(AA q in Q) (EE r in R) (p^3-2q^2+3r
`not phi hArr (EE r in R)(AA q in Q) (EE p in P) (p^3-2q^2+3r>=r^2+2)`
`not phi hArr (EE p in P)(AA q in Q) (EE r in R) (p^3-2q^2+3r>=r^2+2)`
Formuli predikátového počtu `phi=(EE p in P) (AA q in Q)(EE r in R) (p^3-2q^2+3r>r^2+2)` negujte, potom maximální zjednodušení negace formule `phi` je
`not phi hArr (AA r in R) (EE q in Q)(AA p in P) (p^3-2q^2+3r <=r^2+2)`
`not phi hArr (AA p in P)(EE q in Q)(AA r in R) (p^3-2q^2+3r
`not phi hArr (AA r in R) (EE q in Q)(AA p in P) (p^3-2q^2+3r < r^2+2)`
`not phi hArr (AA p in P)(EE q in Q) (AA r in R) (p^3-2q^2+3r <= r^2+2)`
`not phi hArr (AA r in R) (EE q in Q)(AA p in P) (p^3-2q^2+3r >=r^2+2)`

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