Question

18. If A = (x:x² - 3x + 2 = 0; and
B=(x:x² + 2x - 8 = 0), then (A - B) is
(a) {1,2)
(b) (2)
(c) {1}
(d) {4,3} ​

Answer 1

Answer:

Option C

Step-by-step explanation:

Given:-

A = {x:x² - 3x + 2 = 0}; and

B={x:x² + 2x - 8 = 0}

To find:-

The value of A-B

Solution:-

Given sets are A={x:x² - 3x + 2 = 0}

x²-3x+2=0

=>x²-x-2x+2=0

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

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

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

=>x=1 and 2

A={1,2}

and B={x:x² + 2x - 8 = 0}

x²+2x-8=0

=>x²+4x-2x-8=0

=>x(x+4)-2(x+4)=0

=>(x+4)(x-2)=0

=>x+4=0 or x-2=0

=]x=-4 and 2

B={-4,2}

Now

A-B={1,2}-{-4,2}={1}

Answer:-

A-B={1}

Answer 2

$\large\underline\blue{\bold{Given :-  }}$

• A = {x : x² - 3x + 2 = 0}
• B = {x : x² + 2x - 8 = 0}

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$\large\underline\blue{\bold{To \: Find :-  }}$

• A - B

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Definition :-

Set Difference: The relative complement or set difference of sets A and B, denoted A – B, is the set of all elements in A that are not in B.

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$\large\underline\purple{\bold{Solution :- }}$

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☆ Consider, A = {x : x² - 3x + 2 = 0}

☆ A = {x : x² - 2x - x + 2 = 0}

☆ A = {x : x(x - 2) - 1(x - 2) = 0}

☆ A = {x : (x - 2)(x - 1) = 0}

☆ A = {1, 2}

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☆ Consider, B = {x : x² + 2x - 8 = 0}

☆ B = {x : x² + 4x - 2x - 8 = 0}

☆ B = {x : x(x + 4)x - 2(x - 4) = 0}

☆ B = {x : (x + 4)(x - 2) = 0}

☆ B = {2, - 4}

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Hence, A - B = {1}

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$\large{\boxed{\boxed{\bf{Option \: (c) \: is \: correct}}}}$

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