Provide an appropriate response.
-$[ ( \operatorname { aff } A ) \cup ( \operatorname { aff } B ) ] \subset ( A \cup B )$
What property must the set $( A \cup B )$ have if the above statement is true?
A) There is nothing special about $( \mathrm { A } \cup \mathrm { B } )$. The statement is always true.
B) $( A \cup B )$ must contain collinear points.
C) $\mathrm { A } \subset \mathrm { B }$ so that $( \mathrm { A } \cup \mathrm { B } ) = \mathrm { A }$.
D) $( A \cup B )$ has to be affine.

Question

Quizplus · Accepted Answer

The affine hull of a set, denoted as $\operatorname{aff}(A)$, is the smallest affine space that contains the set. The statement $[ ( \operatorname { aff } A ) \cup ( \operatorname { aff } B ) ] \subset ( A \cup B )$ would only be true if $A \cup B$ itself forms an affine space, meaning it must be closed under affine combinations. This is what being affine implies.

Provide an Appropriate Response [(aff⁡A)∪(aff⁡B)]⊂(A∪B)[ ( \operatorname { aff } A ) \cup ( \operatorname { aff } B ) ] \subset ( A \cup B )[(affA)∪(affB)]⊂(A∪B)

Provide an Appropriate Response $[ ( \operatorname { aff } A ) \cup ( \operatorname { aff } B ) ] \subset ( A \cup B )$