Question

Given sets, I = {x ∈ R: x³ − 6x² + 11x − 6 = 0} and J = { x ∈ R: x² − 2x + 1 = 0}

a. Equal b. Equivalent c. None of these d. J ⊂ I

Answer 1

Answer:

Option d

J ⊂ I

Step-by-step explanation:

Given :-

I= {x ∈ R: x³ − 6x² + 11x − 6 = 0}

J = { x ∈ R: x² − 2x + 1 = 0}

To find :-

Which of the following is true :

a. Equal

b. Equivalent

c. None of these

d. J ⊂ I

Solution :-

Given sets are :

I= {x ∈ R: x³ − 6x² + 11x − 6 = 0}

x³ − 6x² + 11x − 6 = 0

=> x³-x²-5x²+5x+6x-6 = 0

=> (x³-x²)+(-5x²+5x)+(6x-6) = 0

=> x²(x-1)-5x(x-1)+6(x-1) = 0

=>(x-1)(x²-5x+6) = 0

=> (x-1)(x²-2x-3x+6) = 0

=> (x-1)[x(x-2)-3(x-2)]=0

=> (x-1)(x-2)(x-3) = 0

=>x-1 = 0 or x-2 = 0 or x-3 = 0

=> x = 1 or 2 or 3

So ,I ={ 1,2,3}

and

J = { x ∈ R: x² − 2x + 1 = 0}

x²-2x+1 = 0

=> x²-x-x+1 = 0

=> x(x-1)-1(x-1) = 0

=> (x-1)(x-1) = 0

=> x-1 =0 or x-1 = 0

=>x = 1 or x = 1

So J ={1}

So The element of J is in the set I

So J is the sub set of I

J ⊂ I

Answer:-

J is the sub set of I

J ⊂ I ---Option d

Used formulae:-

Let A and B are two sets ,If every element of A in the set B then A is called sub set of B and B is the super set of A.(A⊂ B)

Answer 2

Answer:

full answer is given check it