$$\text { Let } A , B \text {, and } C \text { be sets. Prove or disprove that } A - ( B \cap C ) = ( A - B ) \cup ( A - C ) \text {. }$$

Question

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The Answer is We see that

A - ( B \cap C ) = A \cap \overline { B \cap C } = A \cap ( \bar { B } \cup \bar { C } ) = ( A \cap \bar { B } ) \cup ( A \cap \bar { C } ) = ( A - B ) \cup ( A - C )

. These equalities follow from the definition of the difference of two sets, De Morgan's law, the distributive law for intersection over union, and the definition of the difference of two sets, respectively.

Let A,B, and C be sets. Prove or disprove that A−(B∩C)=(A−B)∪(A−C). \text { Let } A , B \text {, and } C \text { be sets. Prove or disprove that } A - ( B \cap C ) = ( A - B ) \cup ( A - C ) \text {. } Let A,B, and C be sets. Prove or disprove that A−(B∩C)=(A−B)∪(A−C).

Definitions:

$\text { Let } A , B \text {, and } C \text { be sets. Prove or disprove that } A - ( B \cap C ) = ( A - B ) \cup ( A - C ) \text {. }$