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22. Show that (p ^ 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.

22. Show that (p ^ 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.

Advanced Engineering Mathematics
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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Discrete Math - Logical Equivalence. Please help me out, Thankyou so much! 22-23.
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.
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.
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