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Math Help - sets and set notation 3 problems

  1. #1
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    sets and set notation 3 problems

    1. Use set notation to list the elements for natural numbers divisible by 4

    a. {4,44,444, ....}
    b. {..,-8,-4, 0,4,8.....}
    c. {4,8,12.....}
    d. {1,2,3,4.....}


    2. Which of the following is a subset of Z = {5,10,15,20,.....}

    a. {-5,0,5}
    b. {10,20...}
    c. {2,4,6....}
    d. {3,6,9...}

    3. Find the cardinality of the set A = {the letters in the word MATH}

    a. 4
    b. {M,A,T,H}
    c. {B,C,D,E,F,G,I,J,K,L,N,O,P,Q,R,S,U,V,W,X,Y,Z}
    d. 0
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  2. #2
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    Quote Originally Posted by Retiredyoung24@yahoo.com View Post
    1. Use set notation to list the elements for natural numbers divisible by 4

    a. {4,44,444, ....}
    b. {..,-8,-4, 0,4,8.....}
    c. {4,8,12.....}
    d. {1,2,3,4.....}
    (c)
    Because natural numbers as,
    <br />
{0,1,2,3,...<br />
}
    Of these (c) fits the condition though it should have included the element 0.


    2. Which of the following is a subset of Z = {5,10,15,20,.....}

    a. {-5,0,5}
    b. {10,20...}
    c. {2,4,6....}
    d. {3,6,9...}
    (b) any element of form 10k is 5(2k) is also of form 5k.
    3. Find the cardinality of the set A = {the letters in the word MATH}

    a. 4
    b. {M,A,T,H}
    c. {B,C,D,E,F,G,I,J,K,L,N,O,P,Q,R,S,U,V,W,X,Y,Z}
    d. 0
    Cardinality is NOT a set is is a number (finite or infinite) in this case 4.
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  3. #3
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    Quote Originally Posted by Retiredyoung24@yahoo.com View Post
    1. Use set notation to list the elements for natural numbers divisible by 4

    a. {4,44,444, ....}
    b. {..,-8,-4, 0,4,8.....}
    c. {4,8,12.....}
    d. {1,2,3,4.....}
    The answer to this depends on who you talk to. For some \mathbb{N} = \{1, 2, 3,... \} and for others \mathbb{N} = \{0, 1, 2, 3,... \}.

    Presumably your book has the former for the definition of the set of natural numbers. So we can see that option a doesn't contain all natural numbers divisible by 4, b contains negative numbers, and d is just all natural numbers. So the answer is c.

    Quote Originally Posted by Retiredyoung24@yahoo.com View Post
    2. Which of the following is a subset of Z = {5,10,15,20,.....}

    a. {-5,0,5}
    b. {10,20...}
    c. {2,4,6....}
    d. {3,6,9...}
    A subset contains only elements of the set, but may not contain all of them. So a contains negative elements, and c and d contain elements that are not in Z. So the answer is b.

    Quote Originally Posted by Retiredyoung24@yahoo.com View Post
    3. Find the cardinality of the set A = {the letters in the word MATH}

    a. 4
    b. {M,A,T,H}
    c. {B,C,D,E,F,G,I,J,K,L,N,O,P,Q,R,S,U,V,W,X,Y,Z}
    d. 0
    The cardinality of a set with a finite number of elements is just the number of elements. This set has 4 elements, so the answer is a.

    -Dan
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