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Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer ?
Most Upvoted Answer
Show that every positive even integer is of the form 2q, and that ever...
By Euclid's Lemma we know that,
a = 2q + r where, 0 less than or equal to r less than 2
Here, r can be equal or greater than zero but less than 2 at any cost.
This possible values for r can be 0 or 1.
r = 0 and 1
By substituting values of r,
a = 2q and a = 2q + 1
Thus, a will be an even positive integer for 2q.
Similarily, a will be an odd positive integer for 2q + 1.
a = 2q + r where, 0 less than or equal to r less than 2
Here, r can be equal or greater than zero but less than 2 at any cost.
This possible values for r can be 0 or 1.
r = 0 and 1
By substituting values of r,
a = 2q and a = 2q + 1
Thus, a will be an even positive integer for 2q.
Similarily, a will be an odd positive integer for 2q + 1.
Community Answer
Show that every positive even integer is of the form 2q, and that ever...
Let n is the number which is divided by 2 and quotient is q and reminder is r.
n=2q+r (where 0<=r>2)
so, n=2q +0
n=2q+1
2q is an even and 2q +1 is odd integer
n=2q+r (where 0<=r>2)
so, n=2q +0
n=2q+1
2q is an even and 2q +1 is odd integer
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Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer ?
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Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer ?.
Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer ?.
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