Is the following statement true or false? For all integers a, b, and c, if albc then alb or alc. Find values of a, b, and c that can be used (a, b, c) = answer this question and enter them below. When you substitute the values you filled in for (a, b, c), which of the choices below answers the question? O The statement is true. Proof: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a divides b. O The statement is true. Proof: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a divides c. O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc but a does not divide either b or c. O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a also divides b. O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a also divides c. O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a does not divide bc but a divides either b or c.

Is the following statement true or false? For all integers a, b, and c, if albc then alb or alc. Find values of a, b, and c that can be used (a, b, c) = answer this question and enter them below. When you substitute the values you filled in for (a, b, c), which of the choices below answers the question? O The statement is true. Proof: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a divides b. O The statement is true. Proof: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a divides c. O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc but a does not divide either b or c. O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a also divides b. O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a also divides c. O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a does not divide bc but a divides either b or c.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 35E

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Question

Is the following statement true or false?
For all integers a, b, and c, if albc then alb or alc.
Find values of a, b, and c that can be used to answer this question and enter them below.
(a, b, c) =
When you substitute the values you filled in for (a, b, c), which of the choices below answers the question?
O The statement is true. Proof: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a divides b.
O The statement is true. Proof: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a divides c.
O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc but a does not divide either b or c.
O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a also divides b.
O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc and a also divides c.
O The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a does not divide bc but a divides either b or c.

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Follow-up Question

Hello,

I'm having trouble with the following question.

Is the following statement true or false?
For all integers a, b, and c, if a|bc then a|b or a|c.
Find values of a, b, and c that can be used to answer this question and enter them below.
(a, b, c) = ?

the second part i got correctly which is The statement is false. Counterexample: Let a, b, and c be the numbers in the ordered triple above. Then a divides bc but a does not divide either b or c.

however i cannot answer the first part

Solution