Answer to Question #330947 in Discrete Mathematics for Ryuzen

Question

7. Which of the following statement is not a member of set X?

X = {tiger, lion, puma, cheetah, leopard, cougar, ocelot}

 

A. cougar

B. bobcat

C. puma

D. Tiger

 

8. What type of set is H?

 

A. Empty

B. Finite

C. Infinite

D. None of the above.

 

9. Which of the ff. sets are finite?

A. {vowels}

B. {days of the week}

C. {primary colors}

D. All of the above.

 

10. Which of the ff. sets is equal to set P?

P = {Monday, Tuesday, Wednesday, Thursday, Friday}

 

A. W = {Thursday, Friday, Saturday, Sunday, Monday}

B. X = {Tuesday, Wednesday, Thursday, Friday, Saturday}

C. Y = {Thursday, Friday, Monday, Tuesday, Wednesday}

D. All of the Above.

 

II - Truth Table (Make a truth table for the given expression.) 10pts each.

11. (~p∧q) ∨ (p∧~q)

12. (~p∧q) ∨ (~p∨q)

 

III - Set Analysis.

Consider the counting numbers {1,2,3,4,5,6,7,8,9}.

Let A={1,3,5,7,9}, B={2,4,6,8}, C={3,5}

 

13. Find A union B. {A∪B}

14. Find A complement. {A’}

15. Find B intersect C. B∩C}

Answer 1

I.

7. B. bobcat does not belong to $X=\rm\{tiger, lion, puma, cheetah, leopard, cougar, ocelot\}$

8. Set $H$ is not defined. In case it is the same as $X$, it is B. finite. Otherwise, we may assume that it is A. empty.

9.D. All of the above. Namely, a number of vowels is finite. Days of the week and primary colors are also finite sets.

10.$W$ and $X$ are not the same as $P$, because they contain Saturday, which does not belong to $P.$

The answer is C. $Y.$ $P$ and $Y$ contain the same elements but in different order.

II. We assume that ~ denotes negation.

11.

12.

III. Denote: $X=\{1,2,3,4,5,6,7,8,9\}$

13.In order to find the union, we make a set that contains all the elements of $A$ and $B:$

$A\cup B=\{1,2,3,4,5,6,7,8,9\}=X$

14.A complement of $A$ are all the elements that belong to the original set, but do not belong to $A$. We have: $A=\{2,4,6,8\}=B$

15.The intersect includes elements that belong to both sets. Namely, $B\cap C-\empty$.

We enumerate all answers without explanations below:

I.

7.B. bobcat;

8.A. Empty or B. Finite

9.D. All of the above

10.C. $Y$

II

11.

12.

III Denote $X=\{1,2,3,4,5,6,7,8,9\}$

13.$X$

14.$B$

15.$\empty$