Answer

Verified

412.5k+ views

**Hint:**The form $4q + 2$ can be written by $4q + 2 = 2(2q + 1)$.Try to substitute \[q\] for different values of integers. Integer is a set of numbers in the form $\{ - \infty ,...... - 2, - 1,0,1,2,3,4,5,.....\infty \} $ it contains both positive and negative numbers and also 0.Here is the set of positive numbers that are $\{ 1,2,3,4,5,.....\infty \} $

In the above set of positive numbers, if we can substitute \[q\] for different integers, then we get a positive integer, and also we say that the form $4q + 2$ be a positive integer.

**Complete step-by-step answer:**

It is given that, \[q\] is an integer.

Let us consider \[y = 4q + 2\]

We can split into \[y = 2(2q + 1)\]

Substitute the value of $q = \{ - \infty ,...... - 2, - 1,0,1,2,3,4,5,.....\infty \} $ in \[y\], we get

Let us substitute the values randomly,

Consider \[q = - 1\] in \[y\], then

\[y = 2(2( - 1) + 1)\]

\[y = 2( - 2 + 1)\]

\[y = 2( - 1)\]

\[y = - 2\]

Also we consider \[q = 0\] in \[y\], then

\[y = 2(2(0) + 1)\]

\[y = 2(0 + 1)\]

\[y = 2(1)\]

\[y = 2\]

Now we consider \[q = 1\] in \[y\], then

\[y = 2(2(1) + 1)\]

\[y = 2(2 + 1)\]

\[y = 2(3)\]

\[y = 6\]

Also we consider, \[q = 2\] in \[y\], then

\[y = 2(2(2) + 1)\]

\[y = 2(4 + 1)\]

\[y = 2(5)\]

\[y = 10\]

Hence we get the value of

\[y = - 2,y = 2,y = 6,y = 10\]

As we observe the above substitution for \[q\] and result of \[y\], it is given that only even numbers.

If we take \[q\] is negative values, it gives result as \[y\] is negative integer,

If we take \[q\] is zero, it gives result as \[y\] is positive even integer,

If we take \[q\] as positive values, it gives a result as \[y\] is positive even integer.

Hence, we can justify our answer, this form does not give positive integer for every integer because positive integer has positive odd integer, positive even integer.

This form gives only positive even integers but our discussion is about every positive integer has the form $4q + 2$.

Hence we justified our answer.

**Note:**We are discussing the form positive integers, actually such a form exists with the condition.

E.g. If \[\{ n\} _{n = 1}^\infty \] for all positive integers of \[n\], then the sequence gives a positive integer.

If \[\{ n\} _{n = - 1}^{ - \infty }\] for all the negative integers of \[n\], then the sequence gives a negative integer also for zero it is zero integer.

It is followed by only certain conditions.

The form \[4q + 2\] for any values of integer, odd integer is missing that odd number is missing. So the form does not satisfy the condition of positive integer.

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail