Q: If 'No odd numbers are divisible by 2,' which of the following is true?

$$O \cap D = \emptyset$$,\ where\ O = \text{odd numbers},\ D = \text{numbers divisible by 2}$

Q: Suppose 'Every poodle is a dog.' Which of the following is the correct set relationship?

$$P \subseteq D$$,\ where\ P = \text{poodles},\ D = \text{dogs}$

Question 1

Which of the following is the correct symbolic representation for the categorical proposition 'No S are P'?

Accepted Answer

$$S \cap P = \emptyset$$

Question 2

Given the statement 'All whole numbers are integers,' which of the following best describes the relationship between the sets of whole numbers (W) and integers (I)?

Accepted Answer

$$W \subseteq I$$

Question 3

Which Venn diagram best represents the proposition 'Some S are not P'?

Accepted Answer

A diagram where part of set S lies outside of set P.

Question 4

If 'No odd numbers are divisible by 2,' which of the following is true?

Accepted Answer

$$O \cap D = \emptyset$$,\ where\ O = 	ext{odd numbers},\ D = 	ext{numbers divisible by 2}$

Question 5

Which of the following is a correct translation of the statement 'Some mathematicians are women' into a categorical proposition?

Accepted Answer

Some M are W, where M = mathematicians and W = women.

Question 6

Suppose 'Every poodle is a dog.' Which of the following is the correct set relationship?

Accepted Answer

$$P \subseteq D$$,\ where\ P = 	ext{poodles},\ D = 	ext{dogs}$

Question 7

If 'Monkeys don't gamble,' which of the following categorical propositions best represents this statement?

Accepted Answer

No M are G, where M = monkeys and G = gamblers.

Question 8

Which of the following is the correct symbolic notation for the union of sets A and B?

Accepted Answer

$$A \cup B$$

Question 9

Given the statement 'Some people don't like chocolate,' which of the following is the correct categorical proposition?

Accepted Answer

Some P are not C, where P = people and C = people who like chocolate.

Question 10

If $$A = \{1, 2, 3, 4\}$$ and $$B = \{3, 4, 5, 6\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{3, 4\}$$

Question 11

Which of the following statements is true about the empty set $$\emptyset$$?

Accepted Answer

$$\emptyset \subseteq S$$\ for\ any\ set\ S$

Question 12

If $$S = \{x | x 	ext{ is a student at the university}\}$$ and $$P = \{x | x 	ext{ is an athlete}\}$$, what does the proposition 'Some S are P' mean?

Accepted Answer

There exists at least one student at the university who is also an athlete.

Question 13

Which of the following is NOT a standard categorical proposition?

Accepted Answer

All S are not P.

Question 14

If $$A = \{2, 4, 6\}$$ and $$B = \{1, 2, 3, 4, 5, 6\}$$, which of the following is true?

Accepted Answer

$$A \subseteq B$$

Question 15

Which of the following best describes the intersection of two sets $$A$$ and $$B$$?

Accepted Answer

The set of all elements that are in both $$A$$ and $$B.$$

Question 16

Suppose 'Some retired people do not work at Walmart.' Which of the following is the correct symbolic representation?

Accepted Answer

Some R are not W, where R = retired people and W = people who work at Walmart.

Question 17

If $$A = \{x | x 	ext{ is a prime number less than 10}\}$$ and $$B = \{x | x 	ext{ is an even number less than 10}\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{2\}$$

Sets, Venn Diagrams, and Categorical Propositions

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