Question

multiple choice. choose the one alternative that best completes the statement or answers the question. write the set in set - builder notation. 1) {2, 4, 6, 8} a) {x | x is any even natural number} b) {2, 4, 6, 8} c) {x | x is an even natural number less than 10} d) {x | x is any even integer less than 10} 2) {2, 4, 8, 16, 32, ...} a) {x | x is a positive integer power of 2} b) {x | x is a positive multiple of 4} c) {x | x is an integer power of 2} d) {x | x is a positive multiple of 2} list the elements in the set. 3) {x | x is a counting number less than -2} a) ∅ b) {-1, 0, 1, ...} c) {-3, -4, -5, ...} d) {..., -5, -4, -3} write the set in set - builder notation. 4) {16, 17, 18, 19} a) {16, 17, 18, 19} b) {x | x is an integer less than 20} c) {x | x is an integer between 16 and 19} d) {x | x is an integer between 15 and 20} 5) {12, 15, 18, 21, ..., 42} a) {x | x is a multiple of 3} b) {x | x is a multiple of 3 between 9 and 45} c) {x | x is a multiple of 3 between 12 and 42} d) {x | x is a multiple of 3 greater than 12} identify the set as finite or infinite. 6) {9, 10, 11, ..., 36} a) infinite b) finite 7) {x | x is an odd counting number} a) infinite b) finite find n(a) for the set. 8) a = {700, 701, 702, ..., 7000} a) n(a)=7000 b) n(a)=4 c) n(a)=6301 d) n(a)=6300 9) a = {x | x is a second in a minute} a) n(a)=120 b) n(a)=infinite c) n(a)=60 d) n(a)=12 10) a = {-8, -7, -6, ..., 0} a) n(a)=8 b) n(a)=9 c) n(a)=1 d) n(a)=4

Explanation:

Step1: Analyze set {2, 4, 6, 8}

The set contains even natural numbers less than 10. Option C correctly describes it in set - builder notation.

Step2: Analyze set {2, 4, 8, 16, 32, ...}

These are positive integer powers of 2. Option A is the correct set - builder notation.

Step3: Analyze set {x | x is a counting number less than - 2}

Counting numbers are positive integers. There are no counting numbers less than - 2, so the set is the empty set $\varnothing$. Option A is correct.

Step4: Analyze set {16, 17, 18, 19}

These are integers between 15 and 20. Option D is the correct set - builder notation.

Step5: Analyze set {12, 15, 18, 21, ..., 42}

These are multiples of 3 between 9 and 45. Option B is the correct set - builder notation.

Step6: Analyze set {9, 10, 11, ..., 36}

It has a definite start and end, so it is a finite set. Option B is correct.

Step7: Analyze set {x | x is an odd counting number}

There are infinitely many odd counting numbers, so it is an infinite set. Option A is correct.

Step8: Analyze set A = {700, 701, 702, ..., 7000}

Use the formula $n(A)=7000 - 700+1=6301$. Option C is correct.

Step9: Analyze set A = {x | x is a second in a minute}

There are 60 seconds in a minute, so $n(A) = 60$. Option C is correct.

Step10: Analyze set A = {- 8, - 7, - 6, ..., 0}

Use the formula $n(A)=0-(-8)+1 = 9$. Option B is correct.

Answer:

1. C. {x | x is an even natural number less than 10}
2. A. {x | x is a positive integer power of 2}
3. A. $\varnothing$
4. D. {x | x is an integer between 15 and 20}
5. B. {x | x is a multiple of 3 between 9 and 45}
6. B. Finite
7. A. Infinite
8. C. n(A) = 6301
9. C. n(A) = 60
10. B. n(A) = 9