plz give me the correct answer I am preparing for mains
Answers
Answer :
Option A
A × (B ∩ C) = { (2 , 4) , (3 , 4) }
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) .
★ Cartesian Product : If A and B are any two non empty sets then the set of all ordered pairs (a,b) such that a € A and b € B is called the cartesian product of sets a with set B and it is denoted by A×B .
→ A×B = { (a,b) : a € A and b € B } .
Solution :
→ Given : • A = { x : x² - 5x + 6 = 0 }
• B = { 2 , 4 }
• C = { 4 , 5 }
→ To find : • A × (B ∩ C)
Firstly ,
Let's find the elements of set A .
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
Thus ,
A = { 2 , 3 }
Now ,
=> B ∩ C = { 2 , 4 } × { 4 , 5 }
=> B ∩ C = { 4 }
Thus ,
=> A × (B ∩ C) = { 2 , 3 } × { 4 }
=> A × (B ∩ C) = { (2 , 4) , (3 , 4) }