Question

if A = {1,2,3,4} and B = {3,6,9} find XUY and X-Y​

Answer 1

Answer :

AUB = {1 , 2 , 3 , 6 , 9}

A - B = {1 , 2 , 4}

Note :

★ 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 = {1 , 2 , 3 , 4} , B = {3 , 6 , 9}
• To find : AUB = ? , A - B = ?

• AUB = {1 , 2 , 3 , 4} U {3 , 6 , 9}

→ AUB = {1 , 2 , 3 , 6 , 9}

• A - B = {1 , 2 , 3 , 4} - {3 , 6 , 9}

→ A - B = {1 , 2 , 4}

Hence ,

AUB = {1 , 2 , 3 , 6 , 9}

A - B = {1 , 2 , 4}