mathematics help


label Calculus
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Jun 1st, 2014
...
Jun 1st, 2014
Nov 21st, 2017
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