Note: This is not asking which statements are true and which are false. It isask

Question

Note: This is not asking which statements are true and which are false. It isasking which statements are logically equivalent to the given statement. Itmight be helpful to let P represent the hypothesis of the given statement, Q represent the conclusion, and then determine a symbolic rep resentation for each statement. Instead of using truth tables, try to use alr eady established logical equivalencies to justify your conclusions

11. Let a; b, and 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 th is conditional statement and which ones are negations of this conditional s tatement? The note for Exercise (10) also applies to this exercise.

(a) If a divides b or a divides c , then a divides bc.

(b) If a does not divide b or a does not divide c , then a does not divide bc.

(c) a divides bc , 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.

Explanation / Answer

(a) ,(d) (f) and (g) similar meaning statementa

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.