6. Write the following statements in terms of p, q, r, and logical connectives. (a) If1 am not in a good mood, then I will go to a movie. (b) I will not go to a movie and I will study discrete structures, (c) I will go to a movie only if I will not study discrete structures.
6. Write the following statements in terms of p, q, r, and logical connectives. (a) If1 am not in a good mood, then I will go to a movie. (b) I will not go to a movie and I will study discrete structures, (c) I will go to a movie only if I will not study discrete structures.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
In Exereises 6 and 7, let p, q, and r be the following state-
ments: p: I will study discrete structure; q: I will go to a
movie; r: I am in a good mood.
6. Write the following statements in terms of p, q, r, and
logical connectives.
(a) If1 am not in a good mood, then I will go to a movie.
(b) I will not go to a movie and I will study discrete
structures,
(c) I will go to a movie only if I will not study discrete
structures.
(d) IfI will not study discrete structures, then I am not in
a good mood.
Transcribed Image Text:13. If p = q is false, can you determine the truth value of
(~(p^q)) = q? Explain your answer.
14. If p = q is false, can you detemine the truth value of
(~p) v (p e q)? Explain your answer.
Transcribed Image Text:rcises 1 and 2, use the following: p: I am awake; q: I
tard; r: I dream of home.
(c) I do not work hard only if I am awake and I do not
dream of home.
(d) Not being awake and dreaming of home is sufficient
for me to work hard.
/rite each of the following statements in terms of p, q,
and logical connectives.
1) I am awake implies that I work hard.
») I dream of home only if I am awake.
) Working hard is sufficient for me to be awake.
I) Being awake is necessary for me not to dream of
3. State the converse of each of the following implications.
(a) If 2+2 = 4, then I am not the Queen of England.
(b) If I am not President of the United Sates, then I will
walk to work.
(c) If I am late, then I did not take the train to work.
home.
(d) If I have time and I am not too tired, then I will go to
the store.
Irite each of the following statements in terms of p, q,
and logical connectives.
1) I am not awake if and only if I dream of home.
) If I dream of home, then I am awake and I work hard.
(e) If I have enough money, then I will buy a car and I
will buy a house.
4. State the contrapositive of each implication in Exercise 3.
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