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A group of five applicants for a pair of identical jobs consists of three men and two women. The employer is to select two of the five applicants for the jobs. Let S denote the set of all possible outcomes for the employer’s selection. Let A denote the subset of outcomes corresponding to the selection of two men and B the subset corresponding to the selection of at least one woman. List the outcomes in A, B, A ∪ B, A ∩ B, and A ∩ B. (Denote the different men and women by M1, M2, M3 and W1, W2, respectively.)

Respuesta :

Answer:

A= {M1,M2},{M2,M3}, {M2,M3}

A U B = S

A n B = 0

A n B'= A

Step-by-step explanation:

A= ( Two males) = { (M1,M2), (M2,M3), (M2,M3)

B= (Atleast one female) = {M1,W1}, {M,W1}, {M3,W1}, {M1,W2} , {M2,W2}, {M3,W2}

Following are the solution to the required function:

Set function:

Given that there are five applicants with three men and two women.

Let S be the subset of the set of all possible outcomes,

[tex]\{M_1, M_2\}, \{M_2, M_3\},\{M_3,M_1\},\{W_1,M_1\},\{W_2,M_1\},\{W_1, M_2\},\\\{W_2,M_2\},\{W_1, M_3\},\{W_2, M_2\}, \{W_1,W_2\}[/tex]

Let A denote the subset of outcomes corresponding to the selection of two men.

The possible outcomes of A are,

[tex]\{M_1,M_2\}, \{M_2,M_3\},\{M_3,M_1\}[/tex]

Let B be the subset corresponding to the selection of at least one woman.

[tex]\{W_1,M_1\},\{W_2,M_1\},\{W_1, M_2\},\\\{W_2,M_2\},\{W_1, M_3\},\{W_2, M_2\}, \{W_1,W_2\}[/tex]

Then [tex]\bar{B} =[/tex]

[tex]\{M_1,M_2\}, \{M_2,M_3\},\{M_3,M_1\}[/tex]

Find [tex]A\cup B\\\\[/tex]

[tex]=\{\{M_1,M_2\}, \{M_2,M_3\},\{M_3,M_1\}\} \cup \{ \{W_1,M_1\},\{W_2,M_1\},\{W_1, M_2\},\\\{W_2,M_2\},\{W_1, M_3\},\{W_2, M_2\}, \{W_1,W_2\}\}\\\\=\{\{M_1,M_2\}, \{M_2,M_3\},\{M_3,M_1\}, \{W_1,M_1\},\{W_2,M_1\},\{W_1, M_2\},\\\{W_2,M_2\},\{W_1, M_3\},\{W_2, M_2\}, \{W_1,W_2\}\}\\\\[/tex]

Find [tex]A\cap B\\\\[/tex]

[tex]=\{\{M_1,M_2\}, \{M_2,M_3\},\{M_3,M_1\}\} \cap \{ \{W_1,M_1\},\{W_2,M_1\}, \{W_1, M_2\}, \\ \{W_2,M_2\},\{W_1, M_3\},\{W_2, M_2\}, \{W_1,W_2\}\}\\\\ =\{\phi\}[/tex]

Find [tex]A\cap \bar{B}\\\\[/tex]

[tex]=\{\{M_1,M_2\}, \{M_2,M_3\},\{M_3,M_1\}\cap\{\{M_1,M_2\}, \{M_2,M_3\},\{M_3,M_1\}\\\\=\{\{M_1,M_2\}, \{M_2,M_3\},\{M_3,M_1\}\\\\[/tex]

Learn more about the set function here:

brainly.com/question/25009504

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