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3.7.15. (a) Is the statement P >Q logically equivalent to (¬P) → (¬Q) ? Explain. (b) Is the statement (PA Q) V R equivalent to PA (Q v R) ? Explain. (c) Is the statement (P → Q) = R equivalent to P → (Q → R) ? Explain.

3.7.15. (a) Is the statement P >Q logically equivalent to (¬P) → (¬Q) ? Explain. (b) Is the statement (PA Q) V R equivalent to PA (Q v R) ? Explain. (c) Is the statement (P → Q) = R equivalent to P → (Q → R) ? Explain.

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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3.7.13. (a) Find a statement that is equivalent to -(PA(-Q)), which is a disjunction (i.e., incl symbol V). (b) Write a statement that is equivalent to P Q, using only the connectives V and . 3.7.14. Explain why (PV Q) → R and (P R) ^ (Q → R) are logically equivalent statements avoid truth tables). 3.7.15. (a) Is the statement P → Q logically equivalent to (¬P) → (¬Q) ? Explain. (b) Is the statement (PA Q) V R equivalent to PA (Q v R) ? Explain. (c) Is the statement (P Q) → R equivalent to P→ (Q → R) ? Explain. (d) Is the statement (-P) (¬Q) the negation of P → Q ? Explain. 3.7.16. Write the contrapositive of the following sentences. Use words or the logic symbols, and sir your answer. Try to avoid using the negation symbol, or words of negation. (a) If k is a prime and k # 2, then k is odd. 78 @2017 Shay Fuchs. All rights re
Transcribed Image Text:3.7.13. (a) Find a statement that is equivalent to -(PA(-Q)), which is a disjunction (i.e., incl symbol V). (b) Write a statement that is equivalent to P Q, using only the connectives V and . 3.7.14. Explain why (PV Q) → R and (P R) ^ (Q → R) are logically equivalent statements avoid truth tables). 3.7.15. (a) Is the statement P → Q logically equivalent to (¬P) → (¬Q) ? Explain. (b) Is the statement (PA Q) V R equivalent to PA (Q v R) ? Explain. (c) Is the statement (P Q) → R equivalent to P→ (Q → R) ? Explain. (d) Is the statement (-P) (¬Q) the negation of P → Q ? Explain. 3.7.16. Write the contrapositive of the following sentences. Use words or the logic symbols, and sir your answer. Try to avoid using the negation symbol, or words of negation. (a) If k is a prime and k # 2, then k is odd. 78 @2017 Shay Fuchs. All rights re
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