13. -(р — q) -рл-а 14. (р — q) л(р — г) %3D р — (q л г) 15. (р — г) л (q - г) %3 (pvq) — r
13. -(р — q) -рл-а 14. (р — q) л(р — г) %3D р — (q л г) 15. (р — г) л (q - г) %3 (pvq) — r
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
Related questions
Question
Discrete Math - Logical Equivalence.
Please help me out, Thankyou so much! 13-15
![Show the logical equivalence of the following
7. (p V q) V r = p V (q V r)
8. (рла) лг-рл(q л г)
9. p → q = ¬p V q
10. p → q = ¬q → ¬p
11. p V q = ¬p → q
12. p ^ q = ¬(p
13. -(р
14. (p
15. (p →
16. (р
17. (р
18. p → q
q) = p ^ ¬g
9) л (р
r) A (q → r) = (p V q)
→ r) = p –→ (q A r)
q) v (p
r) V (q
→ r) = p → (q V r)
r) %3D (рлq) —r
(p → q) ^ (q → p)
19. p → q = ¬p → ¬q
20. p + q = (p ^ q) v (¬p ^ ¬g)
21. ¬(p
p + ¬q
22. Show that (p A q)
(p V q) is a tautology
23. Show that ¬(p V (¬p ^ q)) and ¬p ^ ¬q are logically equivalent by developing a series of logical
equivalences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbc58b6a-6c80-43ac-b15e-b818cb2970c0%2Fa53e444d-6a92-42f9-8d80-9352a1cad88f%2Fjz0cx48_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show the logical equivalence of the following
7. (p V q) V r = p V (q V r)
8. (рла) лг-рл(q л г)
9. p → q = ¬p V q
10. p → q = ¬q → ¬p
11. p V q = ¬p → q
12. p ^ q = ¬(p
13. -(р
14. (p
15. (p →
16. (р
17. (р
18. p → q
q) = p ^ ¬g
9) л (р
r) A (q → r) = (p V q)
→ r) = p –→ (q A r)
q) v (p
r) V (q
→ r) = p → (q V r)
r) %3D (рлq) —r
(p → q) ^ (q → p)
19. p → q = ¬p → ¬q
20. p + q = (p ^ q) v (¬p ^ ¬g)
21. ¬(p
p + ¬q
22. Show that (p A q)
(p V q) is a tautology
23. Show that ¬(p V (¬p ^ q)) and ¬p ^ ¬q are logically equivalent by developing a series of logical
equivalences.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,