in the venn diagram, ( x ) means: a {c, d, e, f, g, h} b {b, c, f, e} c {a, b, c, d, e, f, g, h} d {a, d, g, h}

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# Brief Explanations:
The complement of a set $ X $ (denoted as $ X' $) in a universal set $ U $ includes all elements in $ U $ that are not in $ X $. In the Venn diagram, set $ X $ contains elements $ b, c, e, f $. The universal set $ U $ includes all elements $ a, b, c, d, e, f, g, h $. So, $ X' $ will be the elements in $ U $ but not in $ X $, which are $ a, d, g, h $? Wait, no, wait. Wait, let's re - examine. Wait, the set $ X $ is the circle labeled $ X $, so its elements are $ b $ (only in $ X $), $ c $ (in $ X \cap Y $), $ e $ (in $ X \cap Z $), $ f $ (in $ X \cap Y \cap Z $). So the universal set $ U $ has all regions: $ a $ (only in $ Y $), $ b $ (only in $ X $), $ c $ ( $ X \cap Y $ ), $ d $ (only in $ Y $), $ e $ ( $ X \cap Z $ ), $ f $ ( $ X \cap Y \cap Z $ ), $ g $ ( $ Y \cap Z $ ), $ h $ (only in $ Z $ ). So $ X' $ is all elements not in $ X $. So elements not in $ X $ are $ a $ (not in $ X $), $ d $ (not in $ X $), $ g $ (not in $ X $), $ h $ (not in $ X $)? Wait, no, that's option D? Wait, no, wait, maybe I made a mistake. Wait, let's list the elements of $ X $: $ X $ consists of the regions inside the $ X $ circle. So the $ X $ circle has $ b $ (only $ X $), $ c $ ( $ X \cap Y $ ), $ e $ ( $ X \cap Z $ ), $ f $ ( $ X \cap Y \cap Z $ ). So the elements not in $ X $ are the elements in $ U $ but outside $ X $. So $ U $ has $ a, b, c, d, e, f, g, h $. Removing $ b, c, e, f $ (elements of $ X $), we get $ a, d, g, h $. Wait, but option D is $ \{a, d, g, h\} $. Wait, but let's check the options again. Option A: $ \{c, d, e, f, g, h\} $ – no, because $ c $ and $ e $ and $ f $ are in $ X $. Option B: $ \{b, c, f, e\} $ – that's $ X $ itself. Option C: $ \{a, b, c, d, e, f, g, h\} $ – that's $ U $. Option D: $ \{a, d, g, h\} $ – these are elements not in $ X $. So the correct answer is D? Wait, no, wait, maybe I messed up the regions. Wait, the $ Y $ circle: $ a $ (outside $ X $ and $ Z $, inside $ Y $), $ d $ (only $ Y $), $ c $ ( $ X \cap Y $ ), $ f $ ( $ X \cap Y \cap Z $ ), $ g $ ( $ Y \cap Z $ ). The $ Z $ circle: $ h $ (only $ Z $), $ e $ ( $ X \cap Z $ ), $ f $ ( $ X \cap Y \cap Z $ ), $ g $ ( $ Y \cap Z $ ). The $ X $ circle: $ b $ (only $ X $), $ c $ ( $ X \cap Y $ ), $ e $ ( $ X \cap Z $ ), $ f $ ( $ X \cap Y \cap Z $ ). So the universal set $ U $ is the rectangle, so all elements $ a, b, c, d, e, f, g, h $. The complement of $ X $, $ X' $, is all elements in $ U $ not in $ X $. So elements not in $ X $ are $ a $ (in $ Y $, not $ X $), $ d $ (in $ Y $, not $ X $), $ g $ (in $ Y \cap Z $, not $ X $), $ h $ (in $ Z $, not $ X $). So $ X'=\{a, d, g, h\} $, which is option D. Wait, but earlier I thought maybe I was wrong, but now it seems correct. Wait, but let's check the options again. Option D is $ \{a, d, g, h\} $, so that's the complement of $ X $.
# Answer:
D. $\{a, d, g, h\}$

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