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Five applicants (Jim, Don, Mary, Sue, and Nancy) are available for two identical jobs. A supervisor selects two applicants to fill these jobs.

  1. Let A denote the set of selections containing at least one male. How many elements are in A?
  2. Let B denote the set of selections containing exactly one male. How many elements are in B?
  3. Write the set containing two females in terms of A and B.
  4. List the elements in A ̅, AB, $A\cup B$, and (AB) ̅.
  • 6
    Posting in the imperative is extremely rude. Give us *one* good reason not to immediately dismiss you as some person who just wants "The Internet" to do his/her homework for him/her.2012-01-16
  • 2
    Nancy and Sue are strange names for males, and Jim is a very strange name for a female.2012-01-16
  • 4
    @Asaf, whatsamatter, not a fan of Johnny Cash? http://en.wikipedia.org/wiki/A_Boy_Named_Sue2012-01-16
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    @user, it is traditional on m.se for posters to indicate how far they have gotten on the questions they ask, where exactly they are stuck, etc., so as to make it easier for us to render useful assistance.2012-01-16
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    Hint: I don't know what notation you use for sets. I will use $\{a,b\}$ for the set that consists of $a$ and $b$ (where $a\ne b$). Note that $\{a,b\}=\{b,a\}$. Now **just list**. For brevity I will use $P$, $Q$, $X$, $Y$, $Z$ as names, where the first two are the males. For question 2, the answer is $\{\{P,X\}, \{P,Y\},\{P,Z\}, \{Q,X\}, \{Q,Y\},\{Q,Z\} \}$. Now count. There are $6$. (There are ways to count without explicitly listing. That will come soon in your course.) For 3, you want the *complement* of $A$.2012-01-16

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