Question

Sa se determine multimea A={x E Z | 6/2x-3 E Z}.​

Answer 1

A = {x ∈ ℤ⏐ 6/(2x-3) ∈ ℤ}

2x-3 ∈ D₆ ⇔ 2x-3 ∈ {-6,-3,-2,-1,1,2,3,6}⏐+3

⇔ 2x ∈ {-3,0,1,2,4,5,6,9} ⏐: 2

⇔ x ∈ {-3/2, 0, 1/2, 1, 2, 5/2, 3, 9/2}

⇒ A = {0, 1, 2, 3}