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

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

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

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

E = The set of all letters in the word TRIGONOMETRY

F = The set of all the letters in the word BETTER

Answer
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Hint: The given problem is related to set notations. The first four sets are given in set-builder form and the last two sets are given in descriptive form. Find the elements that satisfy the properties given in each sub-problem and write them in roster form.

Complete step-by-step answer:

Before proceeding with the solution, we must know the set-builder notation, descriptive notation and roster notation.

The set builder notation is a notation in which the set is described by using the properties of the elements . For example : Consider the set B = {2, 4, 6, 8, 10}. Here B is a set of elements which are positive and even numbers less than 12. So , the property of the elements of the set is that they are positive even numbers less than 12. So , the set B is represented in set builder form as: B = {x : x is a set of even natural numbers, 0 < x < 12} .

The descriptive notation is a notation in which the property of the elements of a set is described using statements. For example: A = The set of all letters in the word MATHEMATICS.

The roster notation is a notation in which all the elements of a set are listed between a pair of curly brackets { } and the elements are separated by commas. For example: B = {2, 4, 6, 8, 10}

Now, coming to the question.

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

A is a set of integers, which are greater than -3 and are less than 7. The integers satisfying the given property are -2, -1, 0, 1, 2, 3, 4, 5 and 6. So, the set A is given as A = { -2, -1, 0, 1, 2, 3, 4, 5, 6}.

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

B is the set of natural numbers that are less than 6. So, B = {1, 2, 3, 4, 5}.

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

C is a set of two-digit numbers whose sum of digits is equal to 8. So, the digits must be (1,7), or (2,6), or (3,5) or (4,4). So, the numbers formed by the given pair of digits are 17, 71, 26, 62, 35, 53 and 44. So, C = {17, 71, 26, 62, 35, 53, 44}.

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

D is a set of prime factors of 60. The prime factors of 60 are 2,3, and 5. So, D = {2, 3, 5}.

E = The set of all letters in the word TRIGONOMETRY

The letters in the word TRIGONOMETRY are E, G, I, M, N, O, R, T and Y. So, E = { E, G, I, M, N, O, R, T, Y}.

F = The set of all the letters in the word BETTER

The letters in the word BETTER are B, E, R and T. So, F = {B, E, R, T}.

Note: Students generally get confused between set-builder notation of sets and roster notation of sets . Both are different and hence , should not be confused . This confusion can lead to wrong answers .

Complete step-by-step answer:

Before proceeding with the solution, we must know the set-builder notation, descriptive notation and roster notation.

The set builder notation is a notation in which the set is described by using the properties of the elements . For example : Consider the set B = {2, 4, 6, 8, 10}. Here B is a set of elements which are positive and even numbers less than 12. So , the property of the elements of the set is that they are positive even numbers less than 12. So , the set B is represented in set builder form as: B = {x : x is a set of even natural numbers, 0 < x < 12} .

The descriptive notation is a notation in which the property of the elements of a set is described using statements. For example: A = The set of all letters in the word MATHEMATICS.

The roster notation is a notation in which all the elements of a set are listed between a pair of curly brackets { } and the elements are separated by commas. For example: B = {2, 4, 6, 8, 10}

Now, coming to the question.

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

A is a set of integers, which are greater than -3 and are less than 7. The integers satisfying the given property are -2, -1, 0, 1, 2, 3, 4, 5 and 6. So, the set A is given as A = { -2, -1, 0, 1, 2, 3, 4, 5, 6}.

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

B is the set of natural numbers that are less than 6. So, B = {1, 2, 3, 4, 5}.

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

C is a set of two-digit numbers whose sum of digits is equal to 8. So, the digits must be (1,7), or (2,6), or (3,5) or (4,4). So, the numbers formed by the given pair of digits are 17, 71, 26, 62, 35, 53 and 44. So, C = {17, 71, 26, 62, 35, 53, 44}.

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

D is a set of prime factors of 60. The prime factors of 60 are 2,3, and 5. So, D = {2, 3, 5}.

E = The set of all letters in the word TRIGONOMETRY

The letters in the word TRIGONOMETRY are E, G, I, M, N, O, R, T and Y. So, E = { E, G, I, M, N, O, R, T, Y}.

F = The set of all the letters in the word BETTER

The letters in the word BETTER are B, E, R and T. So, F = {B, E, R, T}.

Note: Students generally get confused between set-builder notation of sets and roster notation of sets . Both are different and hence , should not be confused . This confusion can lead to wrong answers .

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