Question

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 this conditional statement, which ones are the negations, and which ones are not neither? Justify your answers using logical equivalences or truth tables.
A) If a does not divide b or a does not divide c, then a does not divide bc.
B) If a does not divide b and a does not divide c, then a does not divide bc.
C) If a divides bc and a does not divide c, then a divides b.
D) If a divides bc or a does not divide b, then a divides c. (e) a divides bc, a does not divide b, and a does not divide c.

Answer 1

Step-by-step explanation:

Given that the logical statement is

"If a divides bc, then a divides b or a divides c"

we can see that a must divide one either b or c from the statement above

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

This is False because a can divide b or c

 B) If a does not divide b and a does not divide c, then a does not divide bc.

this is True for a to divide bc it must divide b or c (either b or c)

C) If a divides bc and a does not divide c, then a divides b.

This is True since a can divide bc and it cannot divide c, it must definitely divide b

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

This is True since a can divide bc and it cannot divide b, it must definitely divide c

E) a divides bc, a does not divide b, and a does not divide c.

This is False for a to divide bc it must divide one of  b or c

Answer 2

Answer:

D

Step-by-step explanation: