Given $A = {0, 1, 2, 4, 5}, B = {0, 2, 4, 6, 8}$ and $C = {0, 3, 6, 9}$ . Find the number of elements in
$A \cap (B \cap C)$

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Solution

Given, $A = {0, 1, 2, 4, 5}, B = {0, 2, 4, 6, 8}$ and $C = {0, 3, 6, 9}$
Intersection of two sets has the elements common in both the sets
So, $B \cap C = {0, 6}$
And, $A \cap (B \cap C) = {0, 1, 2, 4, 5} \cap {0, 6} = {0}$ ....(1)
$∴$ number of elements in $A \cap (B \cap C)$ is $1$ .

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Similar questions

A = {0, 1, 2, 4, 5}

B = {0, 2, 4, 6, 8}

C = {0, 3, 6, 9}

Given A = ${0, 1, 2, 3, 4, 5}, B = {0, 2, 4, 6, 8} a n d C = {0, 3, 6, 9}$ . Show that

(i) $A \cup (B \cup C) = (A \cup B) \cup C$ i.e. the union of sets is associative.

(ii) $A \cap (B \cap C) = (A \cap B) \cap C$ i.e. the intersection of sets is associative.

\cup

\cap

B - (A - C)

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