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Sets

Short Answer Type

11. Write the following sets in the roster form :

A = {x : x is an integer and –3 < x < 7}

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12. Write the following sets in the roster form :

B = {x : x is a natural number less than 6}

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13. Write the following sets in the roster form :

C = {x : x is a two-digit natural number such that the sum of its digits is 8}

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14. Write the following sets in the roster form :

D = {x : x is a prime number which is divisor of 60}

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15. Write the following sets in the roster form :

E = The set of all letters in the word TRIGONOMETRY

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16.

If A ⊆ B, show that:

(a) A ∩ B=A (b) A ∪ B = B

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17. Find A A B for the following pairs of sets :

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18.

Write the following intervals in set-builder form :

(i)-∞ 31 (ii) (-∞, 0) (iii) [-1, ∞) (iv) (3, ∞)

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19.
Write the following sets in the roster form :

(i) A = {jt : x ∊ Z and x is a root of the quadratic equation x² - 3x - 10 = 0}

(ii) B = {x : x ∊ N, -5 < x - 2 < 5}

(iii) C = {x : jc is an odd prime number less than 30}

(i) A = $space space space equals space left curly bracket space straight x space colon space straight x space element of space straight Z right parenthesis$ and x is a root of quadratic equation x²-3x -10 = 0}

Now, x²-3x -10 = 0

$rightwards double arrow$ (x-5) (x+2) = 0

$rightwards double arrow$ x=5, -2 which are both integers.

Hence, A = {-2, 5}

(ii) B= {x :x $space element of space straight N$ , -5 < x-2 < 5}

Now, -5 < x-2 < 5

$rightwards double arrow$ -3 < x < 7

$rightwards double arrow$ x is a natural number between -3 and 7 (exclusive).

Hence, B = {1, 2, 3, 4, 5, 6}

(iii) C = {x : x is an odd prime number less than 30}

$rightwards double arrow$ x = 3, 5, 7, 11, 13, 17, 19, 23, 29

Hence C = { 3, 5, 7, 11, 13, 17, 19, 23, 29}