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

Truth Value Of Statements

  • Thread starter Bashyboy
  • Start date
  • #1
1,421
5
The question is, "Determine the truth value of each of these statements if the domain consists of all integers?"

The statements are:

[itex]\forall n(n^2 \geq 0)[/itex]

[itex]\exists n(n^2=2)[/itex]

[itex]\forall n(n^2\geq n)[/itex]

[itex]\exists n(n^2 less than 0) [/itex]

Does it seem, from reading the question, that I am to determine the truth value of the statement by simply looking at it, or is there some proving process involved?
 

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
180
If you can determine the truth by simply looking at it, that seems fine to me. If this is homework, you may want to write a brief explanation even if you could see that it was true by inspection. For example, for the first statement you might write "this square of any real number is ______, therefore this statement is _______"
 
  • #3
1,421
5
What if I was to prove them? How would I go about that? Any hints? Would negating each statement be a good start?
 
  • #4
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
180
Negation might be useful for some of these. Others will probably be more straightforward to prove directly.

For example, to prove that [itex]n^2 \geq 0[/itex] is true for all integers [itex]n[/itex], try considering the following three cases separately: [itex]n > 0[/itex], [itex]n = 0[/itex], [itex]n < 0[/itex].
 

Related Threads on Truth Value Of Statements

  • Last Post
Replies
4
Views
6K
Replies
1
Views
4K
Replies
4
Views
4K
Replies
3
Views
510
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
390
Top