Exam 8: Sets and Logic

Use Venn diagrams to check the validity of the argument. No politicians are honest. Some dishonest people are found out. Therefore, some politicians are found out.

List all subsets of the given set. Identify any of the subsets that are improper. $\{ 6,8 \}$

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,9\} C=\{2,5,8,9,10\} List all the members of the set. $\overline { A \cap B } \cup C$

Use Venn diagrams to check the validity of the argument. No cats can talk. All cats can meow. Therefore, all animals that meow cannot talk. _______________ ( valid / not valid)

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,7\} C=\{2,5,6,7,10\} List all the members of the set. $A \cup ( B \cap C )$

The negation of the statement "Some cats have fur." is "No cats have fur."

Give the numbers of elements in the region marked I in the figure. $| U | = 800 , | A | = 100 , | B | = 300 , | A \cap B | = 60$

Use Venn diagrams to check the validity of the argument. All mathematicians are eccentrics. All eccentrics are rich. Therefore, all mathematicians are rich.

Tell whether you believe the conjecture is true or false. The sum of two odd numbers is odd.

Use Venn diagrams to check the validity of the argument. Some cats have fur. Floppy has fur. Therefore, Floppy is a cat. __________ ( valid / not valid )