1. {1, 3, 9, 27, 81, ...} - Infinite set. This is an example of a geometric sequence where each term is 3 times the previous term. It goes on indefinitely.
2. {b, c, d, f, g, h, ..., 2} - Infinite set. It continues with letters from the alphabet and ends with the number 2. This set is infinite.
3. {x | x is an odd number at least 35} - Infinite set. This set includes all odd numbers greater than or equal to 35, and there are infinitely many odd numbers in this range.
4. {Ø} - Finite set. This set contains only one element, which is the empty set. The cardinality of this set is 1.
5. {x | x is a whole number and x ≥ 50} - Infinite set. This set includes all whole numbers greater than or equal to 50, which is an infinite set.
Answers & Comments
Answer:
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Step-by-step explanation:
1. {1, 3, 9, 27, 81, ...} - Infinite set. This is an example of a geometric sequence where each term is 3 times the previous term. It goes on indefinitely.
2. {b, c, d, f, g, h, ..., 2} - Infinite set. It continues with letters from the alphabet and ends with the number 2. This set is infinite.
3. {x | x is an odd number at least 35} - Infinite set. This set includes all odd numbers greater than or equal to 35, and there are infinitely many odd numbers in this range.
4. {Ø} - Finite set. This set contains only one element, which is the empty set. The cardinality of this set is 1.
5. {x | x is a whole number and x ≥ 50} - Infinite set. This set includes all whole numbers greater than or equal to 50, which is an infinite set.
Explanation:
Sets 1, 2, 3, and 5 are infinite sets.
Set 4 is a finite set with a cardinality of 1.