• Support PF! Buy your school textbooks, materials and every day products Here!

Nested Quantifier

  • Thread starter Bucs44
  • Start date
57
0
Here is the problem that I'm having trouble solving - I'm not sure where to begin. I need to determine the truth value but don't know how to do that.

Ax3y(x^2 < y + 1)
 

matt grime

Science Advisor
Homework Helper
9,394
3
Perhaps you could write that out in plain english. It might even help you understand how to solve your problem.
 
57
0
For every real number x there exists y, x to the second power is less than y plus 1.

So basically I need to find a number that is less than y + 1
 

matt grime

Science Advisor
Homework Helper
9,394
3
No. Read it out loud inserting all of the words.

For all x there is a y such that the condition x^2<y+1 is true.
 

HallsofIvy

Science Advisor
Homework Helper
41,732
885
In other words, to prove that true, you must prove that for any given x there exist y such that y+ 1>x2. You need to show that, whatever x is you can find a corresponding y.
 
57
0
So if I stated x = 1, then x2 would be 1 and then would or could I say y is 1 as well? Making y + 1=2
 

matt grime

Science Advisor
Homework Helper
9,394
3
Now how can you do this for any x?
 
57
0
That's what I don't get - I'm not sure what numbers I'm supposed to be inputing here. Please help as I'm really confused
 
57
0
After working on this - Is this the answer?

y = x2 + 2x = (x + 1)2 – 1
x < 0 then (x – 1)2 > x2 so y can be x2 – 2x -2
x = 0 then y can be 0
 

matt grime

Science Advisor
Homework Helper
9,394
3
You're not supposed to put any numbers in that's the point.

Let's play a game. I'm thinking of a number x. Can you give me a number y(possibly in terms of x) so that y+1 is definitely larger than x^2?
 
57
0
How about z?
 

Related Threads for: Nested Quantifier

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
3
Views
529
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
2
Views
406
  • Last Post
Replies
7
Views
2K
Top