Science & Mathematics - 4 January 2007

I’m doing homeschooling and need to submit this within this week. So, please help. Thanks


2. Let a, b, c 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?
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Note:
This is not asking which statements are true and which are false. It is asking which statement are logically equivalent to the given statement. It might be helpful to let P represent the hypothesis of the given statement, Q represent the conclusion, and then determine a symbolic representation for each statement. Instead of using truth tables, try to use already established logical equivalencies to justify your conclusions.

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1-If a divides b or a divides c, then a divides bc.
2-If a does not divide b or a does not divide c, then a does not divide bc.
3-a divides bc, a does not divide b, and a does not divide c.
4-If a does not divide b and a does not divide c, then a does not divide bc.
5-a does not divide bc or a divides b or a divides c.
6-if a divides bc and a does not divide c, then a divides b.
7-if a divides bc or a does not divide b, then a divides c.

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