Prove the following by contraposition: If the product of two integers is not div

Question

Prove the following by contraposition:
If the product of two integers is not divisible by an integer n, then neither integer is divisible by n.

(Given the reasoning for the next step, state what we can conclude)(a-f = A-F)

a.Contraposition

b. definition of divisible

c. by substitution

d. by associative rule

e. by definition of divisible

f. Extra match

x = kn where k is also an integer

xy = (kn)y

xy is divisible by n

If the product of two integers is not divisible by an integer n, then neither integer is divisible by n.

If one of two integers is divisible by an integer n, then so is their product.

  xy = (ky)n where ky is an integer

   

a.Contraposition

b. definition of divisible

  

c. by substitution

d. by associative rule

e. by definition of divisible

  

f. Extra match

A.

x = kn where k is also an integer

B.

xy = (kn)y

C.

xy is divisible by n

D.

If the product of two integers is not divisible by an integer n, then neither integer is divisible by n.

E.

If one of two integers is divisible by an integer n, then so is their product.

F.

  xy = (ky)n where ky is an integer

Explanation / Answer

a => D
b => E
c => F
d => B
e => C
f => A

a. Contraposition
   D. If the product of two integers is not divisible by an integer n, then neither integer is divisible by n.

b. definition of divisible
   E. If one of two integers is divisible by an integer n, then so is their product.

c. by substitution
   B. xy = (kn)y

d. by associative rule
   F. xy = (ky)n where ky is an integer

e. by definition of divisible
   C. xy is divisible by n
f. Extra match
   A.x = kn where k is also an integer

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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