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1. Show that (p⇒r) ^ (q→r) = (pv q) →r by making a truth table. 2. Verify one of De Morgan's Laws by making a truth table. You may pick either one you want.

1. Show that (p⇒r) ^ (q→r) = (pv q) →r by making a truth table. 2. Verify one of De Morgan's Laws by making a truth table. You may pick either one you want.

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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Homework Exercises 1. Show that (pr) ^ (qr) = (pv q) →r by making a truth table. 2. Verify one of De Morgan's Laws by making a truth table. You may pick either one you want. 3. Use the specified logical identity to write an equivalent statement to each of the following statements. (a) Use the Double Negative Law to write an equivalent statement to "It is not the case that the lights are not on" (b) Use the Commutative Law to write an equivalent statement to "The dog was not barking and the cat was not purring." (c) Use one of De Morgan's Laws to write an equivalent statement to "I went home and I did not do my homework." (d) Use the Conditional Law to write an equivalent statement to "If it is below freezing, then you will be shivering." (e) Use the Biconditional Law to write an equivalent statement to "A man is a bachelor if and only if he is unmarried." (f) Use one of the Distributive Laws to write an equivalent statement to "Dwight pranked Jim, and Pam laughed or Kevin laughed." 4. Verify the following identities by applying a chain of logical identities. You may use only those identifies in the "basic logical identities" table. Make sure you cite every law used, no matter how obvious the law might be. (a) (p → ¬q) = p ^ q (b) p ^ ((q v¬p) Vr) = p ^ (q vr) (c) (q^¬p) v (p^¬q) =(pq) (d) (p^q) →q = T
Transcribed Image Text:Homework Exercises 1. Show that (pr) ^ (qr) = (pv q) →r by making a truth table. 2. Verify one of De Morgan's Laws by making a truth table. You may pick either one you want. 3. Use the specified logical identity to write an equivalent statement to each of the following statements. (a) Use the Double Negative Law to write an equivalent statement to "It is not the case that the lights are not on" (b) Use the Commutative Law to write an equivalent statement to "The dog was not barking and the cat was not purring." (c) Use one of De Morgan's Laws to write an equivalent statement to "I went home and I did not do my homework." (d) Use the Conditional Law to write an equivalent statement to "If it is below freezing, then you will be shivering." (e) Use the Biconditional Law to write an equivalent statement to "A man is a bachelor if and only if he is unmarried." (f) Use one of the Distributive Laws to write an equivalent statement to "Dwight pranked Jim, and Pam laughed or Kevin laughed." 4. Verify the following identities by applying a chain of logical identities. You may use only those identifies in the "basic logical identities" table. Make sure you cite every law used, no matter how obvious the law might be. (a) (p → ¬q) = p ^ q (b) p ^ ((q v¬p) Vr) = p ^ (q vr) (c) (q^¬p) v (p^¬q) =(pq) (d) (p^q) →q = T
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