Question

(A \ B )∪ C = A \ (B∩ C )for any three sets A,B and C
Is the statement true or false?
Give justification in support of your answer.

Answer 1

Answer on Question #79106–Math– Discrete Mathematics

Question

$(A \setminus B) \cup C = A \setminus (B \cap C)$ for any three sets $A, B$ and $C$. Is the statement true or false? Give justification in support of your answer.

Solution

Consider, for example, sets $A = \{1; 2; 3; 4\}, B = \{1; 2; 3\}, C = \{2; 5\}$.

Note that $A \setminus B = \{4\}$, $(A \setminus B) \cup C = \{2; 4; 5\}$, $B \cap C = \{2\}$, $A \setminus (B \cap C) = \{1; 3; 4\}$.

In this case $(A \setminus B) \cup C \neq A \setminus (B \cap C)$, hence the statement is false.

Answer: the statement is false.

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