Question

Determinati :A∩B;A∪B;A-B;B-A ..DAU 30 de puncte **
1)
A={x∈N\X=2k,k∈N,k<4}
B={y∈N\y=x+2,x∈A}
2)
A={x∈N\2x+3≤9}
B={y∈N\y=2x-1,x∈A};
3)
A={x∈N\3x≤30};
B={y∈N\y=2x+2,x∈A};
4)
A={x∈N\21≤2x-1≤33};
B={x∈N\85≥6x-5>19}
5)
A={x∈Nˣ/x<6}
B={y∈N/y=x+1,x∈A}

Answer 1

k=0,1,2,3⇒x∈{0,2,4,6}⇒A={0,2,4,6}
y={2,4,6,8}                  ⇒B={2,4,6,8}
A∩B={2,4,6}     A∪B={0,2,4,6,8}    A\B={0}       B\A={8}

2x+3≤9⇒2x≤6⇒x≤3⇒x∈{0,1,2,3}⇒A={0,1,2,3}
y=2x-1⇒y={1,3,5}                        ⇒B={1,3,5}
A∩B={1,3}    A∪B={0,1,2,3,5}       A\B={0}         B\A={5}

3x≤30⇒x≤10⇒A={0,1,2,3,4,5.....,10}
y=2x+2         ⇒B={2,4,6,8,10.........22}
A∩B={2,4,6,8,10}    A∪B={0,1,2,3,4,.........22}     A\B={1,3,5,7,9}  
B\A={12,14,16,18,20,22}

21≤2x+1⇒2x≥10     2x+1≤33⇒2x≤32⇒x≤16⇒x={10,11,12........,16}
⇒A={10,11.............16}
85≥6x-5⇒90≥6x⇒x≤15       6x-5>19⇒6x>24⇒x>4⇒B={5,6,7,8,9,......15}
A∩B={10,11,12,13,14,15} A∪B={5,6,7,8,9,10,11,.........,16}
A\B={16}  B\A={5,6,7,8,9}

x={1,2,3,4,5}⇒A={1,2,3,4,5}
y={2,3,4,5,6}⇒B={2,3,4,5,6}
A∩B=(2,3,4,5}       A∪B={1,2,3,4,........,6}  A\B={1}      B\A={6}

Answer 2

1. A={0, 2, 4, 6}      B={2, 4, 6, 8}  
    A∩B={2, 4, 6};   A∪B={0, 2, 4, 6, 8};   A\B={0};  B\A={8}

2. A=0, 1, 2, 3}     B={1, 3, 5}   
    A∩B={1, 3};  A∪B={0, 1, 2, 3, 5};  A\B={0};   B\A=}5};  

3. A={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};  B={2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}  
    A∩B={2, 4, 6, 8, 10};  
    A∪B={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22}  
    A\B={0, 1, 3, 5, 7, 9};  B\A={12, 14, 16, 18, 20, 22} 

4. 21≤2x-1≤33 |+1  ⇒ 22≤2x≤34 |:2  ⇒ 11≤x≤17  ⇒
   A={11, 12, 13, 14, 15,16, 17}     
  85≥6x-5>19 |+5   ⇒ 90≥6x>24 |:6  ⇒ 15≥x>4   ⇒  
  B={5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15}   
  A∩B={11, 12, 13, 14, 15};  
  A∪B={5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17} 
  A\B={16, 17};   B\A={5, 6, 7, 8, 9, 10}; 

5. A={1, 2, 3, 4, 5};    B={2, 3, 4, 5, 6}  
   A∩B={2, 3, 4, 5};   A∪B={1, 2, 3, 4, 5, 6};  A\B={1};   B\A={6}