Question

se considera multimile A={x€Z| 6\x-1€Z} si B={x€Z| 3x+8\x+6€Z}
a)verificati daca -5€A intersectat cu B
b) determinati A intersecat cu B​

Answer 1

Explicație pas cu pas:

6/(x-1)

x-1∈D{6}

x-1∈{-6,-3,-2,-1,1,2,3,6} |+1

x∈{-5,-2,-1,0,2,3,4,7}=A

(3x+8)/(x+6)

x+6 | 3x+8 (1)

x+6 | x+6 *(3)

x+6 | 3x+18 (2)

Cu (2) si (1) efectuam scaderea

x+6 | 10

x+6∈D{10}

x+6∈{-10,-5,-2,-1,1,2,5,10} |-6

x∈{-16,-11,-8,-7,-5,-4,-1,4}=B

A∩B={-5,-2,-1,0,2,3,4,7}∩{-16,-11,-8,-7,-5,-4,-1,4}={-5,-1,4}

Observam ca -5 apartine

Bafta!