Prove that for all integers m, if even then 3m + 5 is odd. i understand everything up to 3m + 5=

zei3s4pf2l

zei3s4pf2l

Answered question

2022-02-11

Prove that for all integers m, if even then 3m + 5 is odd. i understand everything up to
3m + 5=3(2p) + 5
=6p + 5 im

Answer & Explanation

budniji8d1

budniji8d1

Beginner2022-02-12Added 15 answers

Proof:
Let m any odd integer.
The definition of even integer gives,
m=2p
Here, p is also integer.
According to the question,
3m + 5=3(2p) + 5
=6p + 5
=2(3p) + 2(2) + 1
=2(3p + 4) + 1
Let, (3p + 4)=a
Here, a is integer.
The above relation implies that,
3m + 5=2a + 1
The above relation 3m + 5=2a + 1 implies the definition of odd integer.
Therefore, for all integers m, if m is even then 3m + 5 is odd.

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