If A = {2, 3, 4, 8, 10}, B = {3, 4, 5, 10, 12 | vedclass

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(A) Given sets are $A = \{2, 3, 4, 8, 10\}$,$B = \{3, 4, 5, 10, 12\}$,and $C = \{4, 5, 6, 12, 14\}$.First,find $(A \cup B) = \{2, 3, 4, 5, 8, 10, 12\}

Vedclass · Accepted Answer

$\{2, 3, 4, 5, 8, 10, 12\}$

Vedclass · Answer

(A) Given sets are $A = \{2, 3, 4, 8, 10\}$,$B = \{3, 4, 5, 10, 12\}$,and $C = \{4, 5, 6, 12, 14\}$.First,find $(A \cup B) = \{2, 3, 4, 5, 8, 10, 12\}$.Next,find $(A \cup C) = \{2, 3, 4, 5, 6, 8, 10, 12, 14\}$.Now,find the intersection $(A \cup B) \cap (A \cup C) = \{2, 3, 4, 5, 8, 10, 12\} \cap \{2, 3, 4, 5, 6, 8, 10, 12, 14\}$.The common elements are $\{2, 3, 4, 5, 8, 10, 12\}$.Alternatively,using the distributive law,$(A \cup B) \cap (A \cup C) = A \cup (B \cap C)$.$B \cap C = \{4, 5, 12\}$.$A \cup (B \cap C) = \{2, 3, 4, 8, 10\} \cup \{4, 5, 12\} = \{2, 3, 4, 5, 8, 10, 12\}$.

If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$,then $(A \cup B) \cap (A \cup C)$ is equal to:

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