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}

Answer 1

`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`

Answer 2

Null set

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.