Asap ! in the venn diagram, consider u = {whole numbers 1 – 100}. let a represent numbers that are

Asap !
in the venn diagram, consider u = {whole numbers 1 – 100}.
let a represent numbers that are perfect squares, b represent numbers that are perfect cubes, and c represent numbers that are perfect fourths.
which number(s) satisfy a ∩ c?
a.
16, 81
b.
1, 16, 81
c.
1, 4, 9, 16, 25, 36, 49, 81, 100
d.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100


[tex]Asap ! in the venn diagram, consider u = {whole numbers 1 – 100}. let a represent[/tex]

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This Post Has 4 Comments

  1. The question is what numbers satisfy A ∩ C.

    The symbol ∩ means intersection, .i.e. you need to find the numbers that belong to both sets A and C. Those numbers might belong to the set C or not, because that is not a restriction.

    Then lets find the numbers that belong to both sets, A and C.

    Set A: perfect squares from A to 100:

    1^2 = 1
    2^2 = 4
    3^2 = 9
    4^2 = 16
    5^2 = 25
    6^2 = 36
    7^2 = 49
    8^2 = 64
    9^2 = 81
    10^2 = 100

    => A = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

    Set C: perfect fourths

    1^4 = 1
    2^4 = 16
    3^4 = 81

    C = {1, 16, 81?

    As you see, all the perfect fourths are perfect squares, so the intersection of A and C is completed included in A. this is:

    A ∩ C = C or A ∩ C = 1, 16, 81

    On the other hand, the perfect cubes are:

    1^3 = 1
    2^3 = 8
    3^3 = 27
    4^3 = 81

    B = {1, 8, 27, 81}

    That means that the numbers 1 and 81 belong to the three sets, A, B, and C.

    In the drawing you must place the number 16 inside the region that represents the intersection of A and C only, and the numbers 1 and 81 inside the intersection of the three sets A, B and C.

  2. The meaning of the inverted U in this item is intersection. This means that the elements of the set A ∩ C should be a perfect square and also a perfect-fourths. The answer to this item is equal to 1, 16, 81. The answer is letter B. 

  3. b.  1, 16, 81

    Step-by-step explanation:

    A is numbers that are perfect squares and C is numbers that are perfect fourths.

    This means that A∩C is numbers that are both perfect squares and perfect fourths.

    Out of the numbers from 1 to 100, the only ones this applies to is 1 (1² = 1 and 1⁴ = 1), 16 (4² = 16 and 2⁴ = 16) and 81 (9² = 81 and 3⁴ = 81).

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