Question

Write the following sets in the roaster form.
(i) A = {x | x is a positive integer less than 10 and 2x – 1 is an odd number}
(ii) C = {x : x^2 + 7x – 8 = 0, x ∈ R}
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Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

Write the following sets in the roaster form.

(i) A = {x | x is a positive integer less than 10 and 2^x – 1 is an odd number}

(ii) C = {x : x^2 + 7x – 8 = 0, x ∈ R}

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

✴➡️(i) 2^x – 1 is always an odd number for all positive integral values of x since 2x is an even number.

➡️In particular, 2^x – 1 is an odd number for x = 1, 2, … , 9.

➡️Therefore, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}

✴➡️(ii) x^2 + 7x – 8 = 0

➡️(x + 8) (x – 1) = 0

➡️x = – 8 or x = 1

➡️Therefore, C = {– 8, 1}

$\Large\mathcal\green{FOLLOW \: ME}$

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Answer 2

Answer:

✴➡️(i) 2^x – 1 is always an odd number for all positive integral values of x since 2x is an even number.

➡️In particular, 2^x – 1 is an odd number for x = 1, 2, … , 9.

➡️Therefore, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}✔

✴➡️(ii) x^2 + 7x – 8 = 0

➡️(x + 8) (x – 1) = 0

➡️x = – 8 or x = 1

➡️Therefore, C = {– 8, 1}✔