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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) ̅.
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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

1 Answers 1

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Hints:

  • There are ${5 \choose 2}=10 $ possible pairs from the five individuals

  • There are ${3 \choose 2}=3 $ possible pairs from the three females

  • There are ${2 \choose 2}=1 $ possible pair from the two males

  • (1) To have at least one male, you must not have two females

  • (2) To have at exactly one male, you must not have two females and you must not have two males

  • (3) See (1)

  • (4) List the ten possible pairs and see which expressions apply