Question 203178
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A = \{1,\,3,\,5,\,7\}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ B = \{c,\,d\}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ S = \{x\,|\,x\,\in\,\I;\,0\,<\,x\,<\,10\}\normal\,\cup\LARGE\,\{x\,|\,x\text{ is a letter in the word 'dice'}\}]


You didn't specify, but I suspect that *[tex \Large S] is your universe set.  It has to be, otherwise expressions like *[tex \Large A'] don't make any sense.  Given that S is the Universe set, *[tex \Large A'], read 'the complement of A', means "everything that is in S that is NOT in A".  The union of two sets is everything that is in one set and everything in the other set as well.


It will be helpful to first enumerate *[tex \Large S]. First we have a set of integers, larger than zero but less than ten, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ S_1 = \{1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9\}]


and then we have the letters of the word 'dice':


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ S_1 = \{d,\,i,\,c,\,e\}]


Put them all together:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ S = \{1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9,\,d,\,i,\,c,\,e\}]


From that set, cross out each element of *[tex \Large A] and you are left with the complement of *[tex \Large A], or *[tex \Large A']


You should be able to figure out the rest.


Notation: *[tex \Large |] means "such that", *[tex \Large \in] means "is an element of", *[tex \Large \I] is the set of integers.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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