which is the intersection of the sets R={0, 1, 2, 4}, S={4, 9, 12, 13}, T={13, 15, 19, 20}? A {4} B null set C {13}

Question

which is the intersection of the sets R={0, 1, 2, 4}, S={4, 9, 12, 13}, T={13, 15, 19, 20}?

A {4}
B null set
C {13}

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Clara 2 weeks 2021-10-14T02:42:01+00:00 2 Answers 0

Answers ( )

    0
    2021-10-14T02:43:22+00:00

    Answer:

    Null set

    Step-by-step explanation:

    4 intersects sets R and S but not T

    13 intersects sets S and T but not R

    So this would result as a null set.

    0
    2021-10-14T02:43:23+00:00

    Answer:

    R\cap S\cap T= \{ \} \text{ or } \phi \text{ aka null/empty/void set}

    since there is no common element in all the three sets.

    since intersection is associative,

    you can do it in simpler ways as:

     L \cap (R \cap T) = \{0,1,2,3,4\}\cap\left(\{4,9,12,13\}\cap\{13,15,19,20\}\right) \\ =\{0,1,2,3,4\}\cap(\{13\} = \phi

    or

     (L \cap R) \cap T = \left(\{0,1,2,3,4\}\cap\{4,9,12,13\}\right)\cap\{13,15,19,20\} \\ =\{4\}\cap(\{13,15,19,20\} = \phi

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