Expressions in discrete mathematics

Question 1

1 / 1 pts

The expression $A \vee B$ A&vee;B is not true unless A and B are both true propositions.

True

Correct!

False

Question 2

1 / 1 pts

The expression $C \oplus D$ C⊕D cannot be true if C and D have the same truth value.

Correct!

True

False

Question 3

1 / 1 pts

The expression $\neg F$ ¬F always has the opposite truth value from F.

Correct!

True

False

Question 4

1 / 1 pts

The expression $G \Rightarrow H$ G&Rightarrow;H cannot be true if G itself is a false proposition.

True

Correct!

False

Question 5

1 / 1 pts

True or false: $(Q \wedge \neg~Q) \vee (\neg~Q \oplus Q)$ , where Q is the proposition that Arthur Conan Doyle wrote a prime number of Sherlock Holmes stories.

Correct!

True

False

There’s not enough information provided to answer this question, at least not in a reasonable amount of time, and with the facts in my possession.

Question 6

1 / 1 pts

True or false: $P \Rightarrow N$ P&Rightarrow;N, where P is the proposition that pigs can fly, and N is the proposition that there are 192 member states of the United Nations.

Correct!

True

False

There’s not enough information provided to answer this question, at least not in a reasonable amount of time, and with the facts in my possession.

Question 7

1 / 1 pts

If is true for some propositions J and B, then is also definitely true.

Correct!

True

False

Question 8

1 / 1 pts

If $G \Rightarrow W$ G&Rightarrow;W is false for some propositions G and W, then $G \oplus W$ G⊕W is definitelytrue.

Correct!

True

False

Question 9

3 / 3 pts

Find binary values for X and Y such that $(\neg X \oplus Y) \wedge \neg Y$ (¬X⊕Y)&wedge;¬Y is true:

X= 0 , Y= 0

Answer 1:

Correct!

Answer 2:

Correct!

Question 10

3 / 3 pts

Find binary values for A, B, and C, such that $\neg (\neg A \Rightarrow (B \oplus C)) \wedge C$ ¬(¬A&Rightarrow;(B⊕C))&wedge;C istrue:

A= 0 (false) , B= 1 (true) , C= 1 (true)

Answer 1:

Correct!

0 (false)

Answer 2:

Correct!

1 (true)

Answer 3:

Correct!

1 (true)

Question 11

2 / 2 pts

Supposes LOVES(x,y) is the proposition that person x loves person y. Which English sentence is a valid interpretation of the following assertion?

$\forall x \ \exists y \ \text{LOVES}(x,y)$ ∀x&exists;yLOVES(x,y)

Nobody loves me.

I love everybody.

Correct!

Everybody loves somebody.

There’s some lovey dovey person who loves every single person in the world.

No matter who a person is, you can always find somebody who loves them.

Question 12

1 / 1 pts

Let OlympicAthlete(x) be the proposition that x is or was an Olympic athlete, and let Male(x) be the proposition that x personally identifies with the male gender. True or false:

$\forall x \text{ OlympicAthlete}(x) \Rightarrow \text{Male}(x)$ ∀xOlympicAthlete(x)&Rightarrow;Male(x)

True

Correct!

False

Question 13

1 / 1 pts

Let HasMoreTwitterFollowersThan(x,y) be the proposition that Twitter user x has more followers than Twitter user y does (at this moment in time). True or false:

$\exists x \exists y \text{ HasMoreTwitterFollowersThan}(x,y)$ &exists;x&exists;yHasMoreTwitterFollowersThan(x,y)