Question

for 10 class 2nd question​

Answer 1

Here is your answer user.

Answer 2

QuestioN :

Show that any positive odd integer is of the form 6q + 1 , or 6q + 3 , 6q + 5, Where q is some integer.

SolutioN :

We have, General Equation.

$\tt \dagger \: \: \: \: \: \fbox{ a = bq + r.}$

Let the positive integer which is divisible by n.

$\tt \longmapsto n = 6q + r.$

$\tt \dagger \: \: \: \: \: r = 0,1,2,3,4,5. \: \: \: \: \: (r < 6)$

Case 1.

When r = 0.

$\tt \longmapsto n = 6q + 0.$

$\tt \longmapsto n = 6q$

Even.

$\rule{90}2$

Case 2.

When, r = 1.

$\tt \longmapsto n = 6q + 1.$

Odd.

$\rule{90}2$

Case 3.

When, r = 2.

$\tt \longmapsto n = 6q + 2.$

Even.

$\rule{90}2$

Case 4.

When, r = 3.

$\tt \longmapsto n = 6q + 3.$

Odd.

$\rule{90}2$

Case 5.

When, r = 4.

$\tt \longmapsto n = 6q + 4.$

Even.

$\rule{90}2$

Case 6.

When, r = 5.

$\tt \longmapsto n = 6q + 5.$

Odd.

Hence Proved.

6q + 1 , or 6q + 3 , 6q + 5 is odd positive integer.