if A={x:x²–16 =0,x belongs to R} and {x:x²–5+6=0,x belongs to R} then find A U B ,A intersection B,A–B,B–A.
Answers
Answer :
• A U B = { -4 , 2 , 3 , 4 }
• A ∩ B = ∅
• A - B = { -4 , 4 }
• B - A = { 2 , 3 }
Note :
★ Set : A well defined collection of distinct objects is called a set .
★ Union of two sets : The union of two sets A and B is the set of all those elements which are either in A or in B or in both .
→ This set is denoted by A U B .
★ Intersection of two sets : The intersection of two sets A and B is the set of all those elements which are in common in both A and B .
→ This set is denoted by A ∩ B .
★ Difference of sets : The difference of two sets A and B in the order ( also called relative complement of B in A ) is the set of all those elements of A which are not the elements of B .
→ It is denoted by (A - B) .
Solution :
→ Given :
• A = { x : x² - 16 = 0 , x € R }
• B = { x : x² - 5x + 6 = 0 , x € R }
→ To find :
• A U B
• A ∩ B
• A - B
• B - A
Firstly ,
Let's find the elements of set A .
Thus ,
=> x² - 16 = 0
=> x² = 16
=> x = √16
=> x = ± 4
Hence , A = { -4 , 4 }
Secondly ,
Let's find the elements of set B .
Thus ,
=> x² - 5x + 6 = 0
=> x² - 2x - 3x + 6 = 0
=> x(x - 2) - 3(x - 2) = 0
=> (x - 2)(x - 3) = 0
=> x = 2 , 3
Hence , B = { 2 , 3 }
Now ,
→ A U B = { -4 , 4 } U { 2 , 3 }
→ A U B = { -4 , 2 , 3 , 4 }
Now ,
→ A ∩ B = { -4 , 4 } ∩ { 2 , 3 }
→ A ∩ B = ∅
Now ,
→ A - B = { -4 , 4 } - { 2 , 3 }
→ A - B = { -4 , 4 } = A
Now ,
→ B - A = { 2 , 3 } - { -4 , 4 }
→ B - A = { 2 , 3 } = B
Hence ,
• A U B = { -4 , 2 , 3 , 4 }
• A ∩ B = ∅
• A - B = { -4 , 4 }
• B - A = { 2 , 3 }
Answer:
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Step-by-step explanation:
A={-4,4}
B={2,3}
AUB={-4,2,3,4}
A(intersects)B=phi
A-B={-4,4}
B-A={2,3}