Question

If set A = {x: x² - 7x - 8 = 0), set B = {2, 4), set C = {4, 5, 6) then the value of A x (B intercection C) is equal to​

Answer 1

Answer:

A = {x ∈ R : x2 + 6x – 7 < 0}

⇒ x2 + 6x – 7 < 0

⇒ x2 + 7x - x – 7 < 0

⇒ x (x + 7) – 1 (x + 7) < 0

⇒ (x – 1) (x + 7) < 0

∴ A ∈ (-7, 1)

Now, B = {x ∈ R : x2 + 9x + 14 > 0}

⇒ x2 + 9x + 14 > 0

⇒ x2 + 7x + 2x + 14 > 0

⇒ x (x + 7) + 2(x + 7) > 0

⇒ (x + 7) (x + 2) > 0

Step-by-step explanation:

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Answer 2

Answer:

The value of A x (B intersection C) is equal to { (-1,4), (8,4) } ,​

A x (B ∩ C) = { (-1,4), (8,4) }.

Step-by-step explanation:

Given A = {x:x² - 7x - 8 = 0}

x² - 8x + x - 8 = 0

x² - 8x + x - 8 = 0

x ( x - 8 ) + 1 ( x - 8 ) = 0

(x+1)(x-8)=0

x = -1,8.

then the set A = { -1 , 8  } ,

A = { -1 , 8  } , B = { 2, 4} , C = { 4, 5, 6}

A x (B ∩ C)

(B ∩ C) =  { 2, 4} ∩  { 4, 5, 6} = {4}

A x (B ∩ C) =  { -1 , 8 } x  {4} = { (-1,4), (8,4) }

A x (B ∩ C) =  { (-1,4), (8,4) }.

therefore the value of A x (B intersection C) = A x (B ∩ C) =  { (-1,4), (8,4) }.

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