1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
AleksAgata [21]
3 years ago
13

Let C(x) be the statement "x has a cat," let D(x) be the statement "x has a dog," and let F(x) be the statement "x has a ferret.

" Express each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives. Let the domain consist of all students in your class. a) A student in your class has a cat, a dog, and a ferret. b) All students in your class have a cat, a dog, or a ferret. c) Some student in your class has a cat and a ferret, but not a dog. d) No student in your class has a cat, a dog, and a ferret. e) For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.
Mathematics
1 answer:
jek_recluse [69]3 years ago
5 0

Answer:

\mathbf{a)} \left( \exists x \in X\right) \; C(x) \; \wedge \; D(x) \; \wedge \; F(x)\\\mathbf{b)} \left( \forall x \in X\right) \; C(x) \; \vee \; D(x) \; \vee \; F(x)\\\mathbf{c)} \left( \exists x \in X\right) \; C(x) \; \wedge \; F(x) \; \wedge \left(\neg \; D(x) \right)\\\mathbf{d)} \left( \forall x \in X\right) \; \neg C(x) \; \vee \; \neg D(x) \; \vee \; \neg F(x)\\\mathbf{e)} \left((\exists x\in X)C(x) \right) \wedge  \left((\exists x\in X) D(x) \right) \wedge \left((\exists x\in X) F(x) \right)

Step-by-step explanation:

Let X be a set of all students in your class. The set X is the domain. Denote

                                        C(x) -  ' \text{$x $ has a cat}'\\D(x) -  ' \text{$x$ has a dog}'\\F(x) -  ' \text{$x$ has a ferret}'

\mathbf{a)}

Consider the statement '<em>A student in your class has a cat, a dog, and a ferret</em>'. This means that \exists x \in X so that all three statements C(x), D(x) and F(x) are true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

                         \left( \exists x \in X\right) \; C(x) \; \wedge \; D(x) \; \wedge \; F(x)

\mathbf{b)}

Consider the statement '<em>All students in your class have a cat, a dog, or a ferret.' </em>This means that \forall x \in X at least one of the statements C(x), D(x) and F(x) is true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

                        \left( \forall x \in X\right) \; C(x) \; \vee \; D(x) \; \vee F(x)

\mathbf{c)}

Consider the statement '<em>Some student in your class has a cat and a ferret, but not a dog.' </em>This means that \exists x \in X so that the statements C(x), F(x) are true and the negation of the statement D(x) . We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

                      \left( \exists x \in X\right) \; C(x) \; \wedge \; F(x) \; \wedge \left(\neg \; D(x) \right)

\mathbf{d)}

Consider the statement '<em>No student in your class has a cat, a dog, and a ferret..' </em>This means that \forall x \in X none of  the statements C(x), D(x) and F(x) are true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as a negation of the statement in the part a), as follows

\neg \left( \left( \exists x \in X\right) \; C(x) \; \wedge \; D(x) \; \wedge \; F(x)\right) \iff \left( \forall x \in X\right) \; \neg C(x) \; \vee \; \neg D(x) \; \vee \; \neg F(x)

\mathbf{e)}

Consider the statement '<em> For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.' </em>

This means that for each of the statements C, F and D there is an element from the domain X so that each statement holds true.

We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

           \left((\exists x\in X)C(x) \right) \wedge  \left((\exists x\in X) D(x) \right) \wedge \left((\exists x\in X) F(x) \right)

You might be interested in
You have 6 reindeer, Rudy, Jebediab, Ezekiel, Lancer, Gloopin, and Balthazar, and you want to have 5 fly your sleigh. You always
Anna71 [15]
You can arrange your reindeer 30 different ways.
5 0
3 years ago
2/5×8/15 what does it mean
VLD [36.1K]

That's mean you gonna multiply

2*8 and 5*15

16/75


Hint: Multiply numerator by numerator and denominator by denominator .


I hope that's help.

4 0
3 years ago
Read 2 more answers
What is the relative frequency of adults with tickets?
galben [10]
a) 0.34

Hope I helped! ( Smiles )
4 0
3 years ago
Which statement describes how to solve<br> 3x+4 = 3x+4?
Likurg_2 [28]

Answer:

That is a infinite solutions equation, but to solve this you would have to subtract 3x from both sides and you will get 4=4.

Step-by-step explanation:

3x+4=3x+4

<u>-3x    -3x</u>

4=4

5 0
3 years ago
4, − 7 and<br> − 5, 5 on the coordinate plane.
Nezavi [6.7K]

Answer:

what are you supposed to be doing

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • Subtract u from 7, then divide v by the result
    10·1 answer
  • A youth soccer field has an perimeter of 120 meters. The length of the field is
    15·1 answer
  • a jar contains 36 marbles. it has 20 red, 12 black, and 4 green marbles. two marbles are drawn; the first is not returned before
    13·1 answer
  • If the height of the rectangle is 4.8cm
    11·1 answer
  • 2x + y + 3z = 19<br> 3x + 2y + 3z = 19<br> X + 4y + 2z = 9<br> What is the value of x?
    13·2 answers
  • 12x+3y=-9 <br><br>find y- intercept​
    14·1 answer
  • A rectangular prism has a surface area of 25 square feet and a similar rectangular prism has a surface area of 49 square feet. I
    5·1 answer
  • A store is having a sale with 10% off everything.
    9·1 answer
  • What does the quantity 28-8 represent?
    11·1 answer
  • A rectangular prism measures 3ft by 6ft by 5ft. If the dimensions of the box were all quadrupled. How would the surface area of
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!