Description
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).
Explanation & Answer
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.
Review
Review
24/7 Homework Help
Stuck on a homework question? Our verified tutors can answer all questions, from basic math to advanced rocket science!
Similar Content
Related Tags
Ezperanza Rising
by Pam Muñoz Ryan
The Aftermath
by Rhidian Brook
2001 A Space Odyssey
by Arthur Clarke
The Prince
by Niccolò Machiavelli
The Goldfinch
by Donna Tartt
Fahrenheit 451
by Ray Bradbury
Big Little Lies
by Liane Moriarty
The Metamorphosis
by Franz Kafka
The Old Man and the Sea
by Ernest Hemmingway