Question

List the elements in each set:

{ x ,|, x , {is an even natural number less than 20} \}{x∣xis an even natural number less than 20}

{ x ,|, x , {is a natural number greater than 6} \}{x∣xis a natural number greater than 6}

{ x ,|, x , {is an odd natural number greater than 11} \}{x∣xis an odd natural number greater than 11}

{ x ,|, x , {is an odd natural number less than 14} \}{x∣xis an odd natural number less than 14}

{ x ,|, x , {is an even natural number between 4 and 79} \}{x∣xis an even natural number between 4 and 79}

{ x ,|, x , {is an odd natural number between 12 and 57} \}{x∣xis an odd natural number between 12 and 57}

Answer 1

The sets consist of natural numbers that fulfill specific conditions such as being even or odd and within certain numerical ranges.

Step-by-step explanation:

The student is asking to list the elements of various sets defined by different conditions related to natural numbers and their properties, such as being even, odd, and within certain ranges. In mathematical terms, these are described using set builder notation. Here are the elements of each set:

• The set of even natural numbers less than 20 is: {2, 4, 6, 8, 10, 12, 14, 16, 18}.
• The set of natural numbers greater than 6 is: {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}.
• The set of odd natural numbers greater than 11 is: {13, 15, 17, 19}.
• The set of odd natural numbers less than 14 is: {1, 3, 5, 7, 9, 11, 13}.
• The set of even natural numbers between 4 and 79 is: {6, 8, 10, 12, 14, ..., 78} (all even numbers in this range).
• The set of odd natural numbers between 12 and 57 is: {13, 15, 17, ..., 55, 57} (all odd numbers in this range).