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 amovie; r: I am in a good mood.6. Write the following statements in terms of p, q, r, andlogical 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 discretestructures,(c) I will go to a movie only if I will not study discretestructures.(d) IfI will not study discrete structures, then I am not ina good mood. 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. rcises 1 and 2, use the following: p: I am awake; q: Itard; r: I dream of home.(c) I do not work hard only if I am awake and I do notdream of home.(d) Not being awake and dreaming of home is sufficientfor 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 of3. 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 willwalk 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 tothe 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 Iwill buy a house.4. State the contrapositive of each implication in Exercise 3.

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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

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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,

structures.

(d) IfI will not study discrete structures, then I am not in

a good mood.

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.

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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