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Write the following sets in the tabular ...

Write the following sets in the tabular from :
(i) `A={x:x` is a positive prime `lt20}`
(ii) `B={x:x` is a natural number `lt10}`
(iii) `C={x:x` is an odd positive ineger and `x^(2)lt30}`
(iv) `D={x:x` is a letter of the Engligh alphabet in the word 'LALLY'}
(v) `E={x"x` is a natural number that divides `24}`

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The correct Answer is:
To write the given sets in tabular form, we will analyze each set one by one. ### Step-by-Step Solution: **(i) Set A:** - We need to find all positive prime numbers less than 20. - The prime numbers less than 20 are: 2, 3, 5, 7, 11, 13, 17, and 19. - Therefore, we can write set A as: \[ A = \{2, 3, 5, 7, 11, 13, 17, 19\} \] **(ii) Set B:** - We need to find all natural numbers less than 10. - The natural numbers less than 10 are: 1, 2, 3, 4, 5, 6, 7, 8, and 9. - Therefore, we can write set B as: \[ B = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \] **(iii) Set C:** - We need to find all odd positive integers such that \(x^2 < 30\). - Let's check the odd positive integers: - For \(x = 1\), \(1^2 = 1 < 30\) (include 1) - For \(x = 3\), \(3^2 = 9 < 30\) (include 3) - For \(x = 5\), \(5^2 = 25 < 30\) (include 5) - For \(x = 7\), \(7^2 = 49 \geq 30\) (do not include 7) - Therefore, we can write set C as: \[ C = \{1, 3, 5\} \] **(iv) Set D:** - We need to find the letters of the English alphabet in the word "LALLY". - The unique letters in "LALLY" are: L, A, Y. - Therefore, we can write set D as: \[ D = \{L, A, Y\} \] **(v) Set E:** - We need to find all natural numbers that divide 24. - The divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24. - Therefore, we can write set E as: \[ E = \{1, 2, 3, 4, 6, 8, 12, 24\} \] ### Final Tabular Form of Sets: - \( A = \{2, 3, 5, 7, 11, 13, 17, 19\} \) - \( B = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \) - \( C = \{1, 3, 5\} \) - \( D = \{L, A, Y\} \) - \( E = \{1, 2, 3, 4, 6, 8, 12, 24\} \)
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