math help

Geology
Tutor: None Selected Time limit: 1 Day

Image text transcribed for accessibility: Which of the following statements are true for all propositions p and q? (True/False)If p q, then p is true or q is false. (True/False)If p q, then p is false or q is true. (True/False)If p q. then (q p). (True/False)If p q then p q. or q p. (True/False) Either p q. or (p q).

Jun 1st, 2014

p->q is the same as "q or not-p"

1.) False.
If for example p is false and q is true, then:
p->q is true,
BUT
neither "p is true" nor "q is false" is true.

2.) True.
By definition of p->q above.

3.) False.
If for examples p and q are both true, then:
p->q is true,
BUT
~(q->p) is false.
[Moral: Just because p->q does not mean that q cannot imply p. An easier example is when p and q are the same statement!]

4.) True.
If BOTH p and q are true, then both implications hold. If EITHER is false, say p is false, then p->q is automatically true. (Similarly, if q is false, then q->p is automatically true.)

5.) True.
This is a tautology. Let r = (p->q), then the statement becomes: r or ~r, which is always true.

Jun 1st, 2014

Are you studying on the go? Check out our FREE app and post questions on the fly!
Download on the
App Store
...
Jun 1st, 2014
...
Jun 1st, 2014
Dec 5th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer