Question

determinati A ∪ B,A ∩ B ,A-B si B-A, PENTRU MULTIMILE .
a)A={a,b.c}.B={b.c.d},
b)A={1,2,3.4},B={x1,2,5,6}
c)A={2,4,6,8,10},B={1,3,5,7}
d)A={x∈N5x-1≤24},B={x∈N/3x+1<15}
e)A={x∈N/7≤x+5<15}.B={x∈N/3<2x+1<15}
f)A={x∈N/xpatrat perfect,x<70},B={x∈N/x cub perfect,x<70}
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Answer 1

  a)   A  U B = { a,b,c,d}, A intersectat B = { b,c}, A-B ={a}, B - A = { d}
  b) A U B ={1,2,3,4,5,6}, A inters. B ={ 2}, A - B ={3,4}, B - A ={5,6}
  c) A U B={1,2,3,4,5,6,7,8,10}, A inters. B ={Ф}, multimea vida, A - B ={2,4,6,8,10}, B - A ={1,3,5,7}
  d) se rezolva inecuatiile pt multimea A si B
     pt. multimea A, Inecuatia 5x - 1 ≤ 24 ⇔ 5x ≤ 24 + 1 ⇔ 5x ≤ 25 ⇔
                              x ≤ 25/5 ⇔ x ≤ 5, x ∈ ( - 00, 5], deci
   x ∈ N si x ∈( - 00, 5} ⇒ x ∈{ 0,1,2,3,4,5}, deci multimea A este
   A = { 0,1,2,3,4,5}
   pt. multimea B, inecuatia 3x + 1< 15⇔3x < 15 - 1⇔ 3x < 14⇒ x< 14/3⇒
   x ∈ ( - 00, 14/3) si x ∈ N ⇒ x ∈ { 0,1,2,3,4}, doar nr/ naturale 14:3 =4,6⇒ deci se iau nr. pana la 4
   B={0,1,2,3,4,5} si A =0,1,2,3,4,5,}⇒ A = B ={0,1,2,3,4,5}
  A U B= {0,1,2,3,4,5}, A inters. B = {Ф}, A- B ={Ф}, B - A ={Ф"