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- Use truth tables to show that (a v b) ^ ((a^ b)) is logically equivalent to a → -b. (This arrangement of T/F values is sometimes called the exclusive or of a and b.)

- Use truth tables to show that (a v b) ^ ((a^ b)) is logically equivalent to a → -b. (This arrangement of T/F values is sometimes called the exclusive or of a and b.)

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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10. Use truth tables to establish the following equivalences. (pv q) is logically equivalent to p^-q. (a) Show that (b) Show that (p^ q) is logically equivalent to -pv-q. These equivalences are known as De Morgan's laws, after the 19th-century logician Augustus De Morgan. 11. Are the statements (pq) and -p -q logically equivalent? Justify your answer using truth tables. 12. Use truth tables to show that (av b)^(-(a^ b)) is logically equivalent to a → ¬b. (This arrangement of T/F values is sometimes called the exclusive or of a and b.)
Transcribed Image Text:10. Use truth tables to establish the following equivalences. (pv q) is logically equivalent to p^-q. (a) Show that (b) Show that (p^ q) is logically equivalent to -pv-q. These equivalences are known as De Morgan's laws, after the 19th-century logician Augustus De Morgan. 11. Are the statements (pq) and -p -q logically equivalent? Justify your answer using truth tables. 12. Use truth tables to show that (av b)^(-(a^ b)) is logically equivalent to a → ¬b. (This arrangement of T/F values is sometimes called the exclusive or of a and b.)
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