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
Basile [38]
3 years ago
11

Let P(x, y) be a propositional function. If Vy3x P(x,y) is true, does it necessarily follow that 3x Vy P(x,y) is true? Justify y

our answer or give a counter-example.
Mathematics
1 answer:
adell [148]3 years ago
3 0

It's not true.

When you say "for all y there exists x such that.." you're saying that x depends on y. In other words, you're saying that you choose any value for y, and then you choose an adequate value for x.

On the other hand, claiming that "there exists x such that, for all y's, ...", you're talking about the existence of a universal value for x, which is "good" for every possible value of y.

Think of this as a role play:

\forall y \exists x: P(x,y)

means that your friend picks a value for y, and you answer choosing a value for x accordingly.

On the other hand,

\exists x:\ \forall y P(x,y)

means that you can pick a value for x that will make you "win" no matter which y-value your friend chooses.

For the counter example: let P(x,y) be "x is the double of y".

It is true that \forall y \exists x: P(x,y)

for every number y your friends chooses, you pick its double: your friend chooses y=4 and you pick x=8, your friend chooses y=-5 and you pick -10, and so on.

But it is not true that you can pick a unique value for x, and that it will be the double of whatever number your friend will pick: if you choose x=6 you will win only if your friend chooses y=3, in all the other cases you will lose.

You might be interested in
James conducted an experiment with 4 possible outcomes. He determined that the experimental probability of event A happening is
Ganezh [65]

Answer:

Completing the experiment a few more times and combining the results to the trails already done.

8 0
3 years ago
Read 2 more answers
Please if someone could help me that would be greatly appreciated.
mariarad [96]

Answer:

Me

Step-by-step explanation:

5 0
3 years ago
What is angle hgf. If angle egf is 110 and angle hge is 3x+11 and angle hgf is 16x+4
Y_Kistochka [10]

Step-by-step explanation:

The Angle Addition Postulate de fusteer Key. Date ... 99° and MZLMF = 36º. Find m2LMN. 6) Find mZWDC if IZEDC = 145° and mZEDW= 61°. N of w. C ... 11) mZHGF = 16x + 4, m EGF = 110°,. 12) mZVUT = 175° ... a H, 16X+4=110 + 3x +11

7 0
2 years ago
A construction worker covered a square floor using 172.3 ft^2 of flooring without any overlap. Which
Drupady [299]

Answer:

Step-by-step explanation:

aye I need the answer soomeine helo me out, add my insta;, hy.cxsar

4 0
3 years ago
The social science that deal with the behavior and thinking of organisms <br> Yes
LUCKY_DIMON [66]

I think it's psychology.

6 0
3 years ago
Read 2 more answers
Other questions:
  • Estimate the quotient 57.8 ÷81
    10·2 answers
  • Which equation represents a line that passes through two points in the table 3,3 and 6,5
    12·1 answer
  • Part 1
    15·1 answer
  • PLEASE HELP IMMEDIATELY
    12·2 answers
  • GPA and study time. A survey was conducted on 218 undergraduates from Duke University who took an introductory statistics course
    13·1 answer
  • Abdullah is buying a dirt bike for $830. He has already paid $200 towards the bike
    11·2 answers
  • Please need help thank you
    13·1 answer
  • Can someone help me it is due today and I’m having trouble
    10·2 answers
  • What is the value of x in the equation −6 + x = −3?
    9·2 answers
  • HELPPPPPPP!!!!!!!!!!!!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!