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The correct match of the following is : ...

The correct match of the following is :
`{:("Column -I",,"Column -II"),((i)"{x:x is an integer and " -3ltxlt7"}",,(a) "{x:x is a prime number and divisor of 6}"),((ii)"{3,4,5,6,7}",,(b)"{4,5,6}"),((iii)"{x:x is a letter of the word MATHEMATICS}",,(d)"finite set"),((iv) "{2,3}",,"{M,A,T,H,E,I,C,S}"):}`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of matching the elements from Column I with those in Column II, we will analyze each element in Column I and find the corresponding match in Column II step by step. ### Step-by-Step Solution: 1. **Identify the first element in Column I:** - **Element (i):** \(\{x : x \text{ is an integer and } -3 < x < 7\}\) - This set includes all integers greater than -3 and less than 7. The integers that satisfy this condition are: \[ -2, -1, 0, 1, 2, 3, 4, 5, 6 \] - Therefore, the set is \(\{-2, -1, 0, 1, 2, 3, 4, 5, 6\}\). 2. **Identify the nature of the set:** - This set is finite since it contains a countable number of elements. 3. **Match with Column II:** - The only option in Column II that describes a finite set is: - **(c)** "finite set". - Thus, we match (i) with (c). 4. **Identify the second element in Column I:** - **Element (ii):** \(\{3, 4, 5, 6, 7\}\) - This is a set of specific integers. 5. **Match with Column II:** - The only option in Column II that matches this set is: - **(b)** \(\{4, 5, 6\}\) (since these are also integers and part of the set). - Thus, we match (ii) with (b). 6. **Identify the third element in Column I:** - **Element (iii):** \(\{x : x \text{ is a letter of the word MATHEMATICS}\}\) - The letters in the word "MATHEMATICS" are: M, A, T, H, E, I, C, S. - The unique letters are: \(\{M, A, T, H, E, I, C, S\}\). 7. **Match with Column II:** - The only option in Column II that describes the letters is: - **(d)** \(\{M, A, T, H, E, I, C, S\}\). - Thus, we match (iii) with (d). 8. **Identify the fourth element in Column I:** - **Element (iv):** \(\{2, 3\}\) - Both 2 and 3 are prime numbers. 9. **Match with Column II:** - The only option in Column II that describes prime numbers and divisors of 6 is: - **(a)** \(\{x : x \text{ is a prime number and divisor of 6}\}\). - Thus, we match (iv) with (a). ### Final Matches: - (i) → (c) - (ii) → (b) - (iii) → (d) - (iv) → (a)
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