(e) a does not divide bc or a divides b or a divides c.

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Author:Erwin Kreyszig
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11. Let a, b, and e be integers. Consider the following conditional statement:
If a divides bc, then a divides b or a divides c.
Which of the following statements have the same meaning as this conditional
statement and which ones are negations of this conditional statement?
The note for Exercise (10) also applies to this exercise.
(a) If a divides b or a divides c, then a divides be.
(b) If a does not divide b or a does not divide c, then a does not divide bc.
(c) a divides be, a does not divide b, and a does not divide c.
* (d) If a does not divide b and a does not divide c, then a does not divide
bc.
(e) a does not divide bc or a divides b or a divides c.
(f) If a divides bc and a does not divide c, then a divides b.
(g) If a divides bc or a does not divide b, then a divides c.
Transcribed Image Text:11. Let a, b, and e be integers. Consider the following conditional statement: If a divides bc, then a divides b or a divides c. Which of the following statements have the same meaning as this conditional statement and which ones are negations of this conditional statement? The note for Exercise (10) also applies to this exercise. (a) If a divides b or a divides c, then a divides be. (b) If a does not divide b or a does not divide c, then a does not divide bc. (c) a divides be, a does not divide b, and a does not divide c. * (d) If a does not divide b and a does not divide c, then a does not divide bc. (e) a does not divide bc or a divides b or a divides c. (f) If a divides bc and a does not divide c, then a divides b. (g) If a divides bc or a does not divide b, then a divides c.
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