Deductive versus Inductive Reasoning



Sets and Set Operations

|Objectives: | |

|Determine if a set is well defined. | |

|Write all the subsets of a given set and label the subsets as proper or improper. | |

|Given a universal set and some subsets, find a complement, intersection or union. | |

|Draw a Venn diagram to illustrate two sets. | |

|Use the cardinal number formula. | |

|Vocabulary: | | |

|roster notation | | |

|set-builder notation | | |

|well defined set | | |

|cardinal number | |Term |

|empty set | |Symbol |

|subset | |Read as |

|proper/improper subset | | |

|intersection of sets | |union |

|union of sets | | |

|mutually exclusive | | |

|complement of a set | | |

| | |intersection |

| | | |

| | | |

| | | |

| | |complement |

| | | |

| | | |

| | | |

| | |subset |

| | | |

| | | |

| | | |

| | | |

| | |Cardinal Number Formula for Union of Sets: |

| | | |

| | | |

| | |Cardinal Number Formula for Complement of a Set: |

| | | |

| | |Symbol |

| | |Term |

| | | |

| | | |

| | |empty set |

| | | |

| | | |

| | |in |

| | | |

| | | |

| | |not in |

| | | |

| | | |

| | |number |

| | | |

Possible Classroom Examples:

Is the given set well-defined?

• the set of all pink automobiles

• the set of all good bands

• the set of odd numbers

• the set of small numbers

Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {0, 2, 4, 5, 6, 8}, and

B = {1, 3, 5, 7, 9}

• Find n(B).

• True or false: [pic]

• True or false: [pic]

• A ( B [pic]

• [pic]

• [pic]

Suppose n(U) = 61, n(A) = 32, n(B) = 26.

• If n(A(B) = 40, find n(A(B) and draw a Venn diagram illustrating the composition of U [pic] [pic]

In a recent health survey, 750 single men in their twenties were asked to check the appropriate box or boxes on the following form:

| | |I am a member of a private gym. [pic] |

| | | |

| | |I am a vegetarian. |

The results were tabulated as follows: 374 checked the gym box, 92 checked the vegetarian box, and 332 were blank (no boxes checked).

a. Draw a Venn diagram illustrating the results of the survey.

b. What percent of these men were both members of a private gym and vegetarians?

Determine how many cards, in an ordinary deck of 52, fit the description.

a. clubs or twos

b. face cards or diamonds

c. threes or sixes

d. threes and sixes

Deck of Cards

|Hearts – Red | |Diamonds – Red |

|[pic] | |[pic] |

|Clubs – Black | |Spades – Black |

|[pic] | |[pic] |

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