Question

let a= {x:x belongs to r, x²-5x+6=0} and {x:x belongs tor, x²=9} Write A and B in roster form and find A union B and A intersection B​

Answer 1

Step-by-step explanation:

Given :-

A= {x:x belongs to R, x²-5x+6=0} and

B={x:x belongs to R, x²=9}

To find :-

i) Write A and B in roster form ?

ii) Find A U B and A n B ?

Solution :-

Given sets are :

A= {x:x belongs to R, x²-5x+6=0}

x²-5x+6 = 0

=> x²-2x-3x+6 = 0

=> x(x-2)-3(x-2) = 0

=> (x-2)(x-3) = 0

=> x-2 = 0 and x-3 = 0

=> x = 2 or x = 3

The roots of x²-5x+6 = 0 are 2 and 3

Roster form of A

A = { 2,3}

and

B={x:x belongs to R, x²=9}

=> x² = 9

=> x =±√9

=> x = ±3

=> x = 3 or -3

Roots of x²=9 are 3 and -3

Roster form of B

B ={-3,3}

Now,

AUB

=> {2,3} U { -3,3}

=> AUB = {-3,2,3}

AnB = {2,3} n { -3,3}

=> AnB = {3}

Answer:-

Roster form of the set A = { 2,3}

Roster form of the set B = { -3,3}

AUB = {-3,2,3}

AnB = {3}

Used formulae:-

• The set of all elements in either A or in B or in both is called The Union of A and B and it is denoted by AUB.

• The set of Common elements in both A and B is called the Intersection of A and B and it is denoted by AnB.

• In Roster form,The list of elements seperating with commas within the braces and it is also called List form .