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24. For all integers a, b, and c, if a b and a c then a (2b-3c). 25. For all integers a, b, and c, if a is a factor of c and b is a factor of c then ab is a factor of c.

24. For all integers a, b, and c, if a b and a c then a (2b-3c). 25. For all integers a, b, and c, if a is a factor of c and b is a factor of c then ab is a factor of c.

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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18. Consider the following statement: The negative of any multiple of 3 is a multiple of 3. a. Write the statement formally using a quantifier and a variable. b. Determine whether the statement is true or false and justify your answer. 19. Show that the following statement is false: For all integers a and b, if 3 (a + b) then 3 (a - b). For each statement in 20-32, determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterex- ample if it is false. H 20. The sum of any three consecutive integers is divis- ible by 3. 21. The product of any two even integers is a multiple of 4. H 22. A necessary condition for an integer to be divisible by 6 is that it be divisible by 2. 23. A sufficient condition for an integer to be divisible by 8 is that it be divisible by 16. 24. For all integers a, b, and c, if a b and a c then a|(2b-3c). 25. For all integers a, b, and c, if a is a factor of c and b is a factor of c then ab is a factor of c. H 26. For all integers a MANNE
Transcribed Image Text:18. Consider the following statement: The negative of any multiple of 3 is a multiple of 3. a. Write the statement formally using a quantifier and a variable. b. Determine whether the statement is true or false and justify your answer. 19. Show that the following statement is false: For all integers a and b, if 3 (a + b) then 3 (a - b). For each statement in 20-32, determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterex- ample if it is false. H 20. The sum of any three consecutive integers is divis- ible by 3. 21. The product of any two even integers is a multiple of 4. H 22. A necessary condition for an integer to be divisible by 6 is that it be divisible by 2. 23. A sufficient condition for an integer to be divisible by 8 is that it be divisible by 16. 24. For all integers a, b, and c, if a b and a c then a|(2b-3c). 25. For all integers a, b, and c, if a is a factor of c and b is a factor of c then ab is a factor of c. H 26. For all integers a MANNE
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