Question

If A = {x/6x² + x -15 = 0}
B = {x/2x² - 5x - 3 = 0}
C = {x/2x² - x- 3} then
find
i) (A ∪ B ∪ C)
ii) (A ∩ B ∩ C)

Answer 1

Answer:

i)  {-5/3, -1, -1/2, 3/2, 3}

ii) Ф

Step-by-step explanation:

Hi,

Given If A = {x/6x² + x -15 = 0}

A is set of all x satisfying 6x² + x -15 = 0

⇒(3x + 5)(2x - 3) = 0

⇒ x = -5/3 or 3/2

so, A = { -5/3, 3/2}

Given B = {x/2x² - 5x - 3 = 0}

B is set of all x satisfying 2x² - 5x - 3 = 0

⇒ (2x + 1)(x - 3) = 0

⇒ x = -1/2 or 3

Hence, B = { -1/2, 3}

Given C = {x/2x² - x- 3 = 0}

C is set of all x satisfying 2x² - x- 3 = 0

⇒(2x - 3)(x + 1) = 0

⇒ x = 3/2 or -1

So, C = { -1, 3/2}

To find  

i) (A ∪ B ∪ C)

= { -5/3, 3/2} ∪ { -1/2, 3} ∪ { -1, 3/2}

= {-5/3, -1, -1/2, 3/2, 3}

ii) (A ∩ B ∩ C)

= { -5/3, 3/2} ∩ { -1/2, 3} ∩ { -1, 3/2}

=Ф (empty set since there is no common element in all 3 sets together.

Hope, it helps !

Answer 2

Answer:

Step-by-step explanation:

First the given sets are written in list form.

Then only we can find out union and intersection easily.

A = {x/6x² + x -15 = 0}

A= {x/(3x+5)(2x-3)=0}

A = {-5/3, 3/2}

B = {x/2x² - 5x - 3 = 0}

B = {x/ (x-3)(2x+1)=0}

B = {3, -1/2}

C = {x/2x² - x- 3}

C ={x/(2x-3)(x+1)=0}

C ={3/2, -1}

i) A∪B∪C

= {-5/3, -1, -1/2, 3/2, 3}

ii)A ∩ B ∩ C

= { }