Question

Daca A ={ x apatine Z-*!2x +3 mai mic sau egal de cat 9} si B = {x apatine Z !3x +7 mai mare sau egal cu 1 calculati Aintersectat cu B si produsele carteziane AxB si BxA .AM PUS 15 puncte .

Answer 1

Răspuns:

A= { 2x+3≤9}= {... -5.-4. -3.-2.-1, 0,1,2,3]

B= { 3x+7≥1}= {-2, -1, 0, 1,2, 3,4...}

2x+3≤9   2x≤6  x≤6:2   x≤3    x∈(-∞, 3]

3x+7≥1    3x≥-6   x≥-6:3   x≥-2   x∈[-2,∞)

A∩B= [-2, 3]

AxB= {(-5,-2); (-5, -1); (-5, 0); (-5,1); (-5,2); (-5,3); ...(3,-2);(3,-1); (3,0);(3,1);(3,2);(3,3)}

BxA={(-2,-5); (-2,-4)...(2,-5);(2,-4)...(4,-5);(4,3)}