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7) Prove the following. a) (pAq) →r = (p-r)v(q-r) b) p-(q-r) = (pr)

7) Prove the following. a) (pAq) →r = (p-r)v(q-r) b) p-(q-r) = (pr)

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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Exercises (Cont'd) 6) Show that each of these conditional statements is a tautology without using truth tables. a) (p p b) -p→ (-p v¬q) c) p→ ("p → -q) 7) Prove the following. a) (pAq) r = (p-r)v(q-r) b) p-(q→r) = (r) 8) Find the value of p, q and r for which the statement (pv¬q) → [r+(p^q)] is false.
Transcribed Image Text:Exercises (Cont'd) 6) Show that each of these conditional statements is a tautology without using truth tables. a) (p p b) -p→ (-p v¬q) c) p→ ("p → -q) 7) Prove the following. a) (pAq) r = (p-r)v(q-r) b) p-(q→r) = (r) 8) Find the value of p, q and r for which the statement (pv¬q) → [r+(p^q)] is false.
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