Please, I need complete detailed proof of the following: Let n be an integer. Th
ID: 2940258 • Letter: P
Question
Please, I need complete detailed proof of the following: Let n be an integer. Then the following four statements areequivalent: (a) n is odd (b) n2 is odd (c) (n-1)2 is even (d) (n+1)2 is even Please, I need complete detail of this proof of each step.Thank you Please, I need complete detailed proof of the following: Let n be an integer. Then the following four statements areequivalent: (a) n is odd (b) n2 is odd (c) (n-1)2 is even (d) (n+1)2 is even Please, I need complete detail of this proof of each step.Thank youExplanation / Answer
QuestionDetails: Please, I need complete detailed proof of the following: Let n be an integer. Then the following four statements areequivalent: (a) n is odd (b) n2 is odd...TRUE=[2P+1]2=4P2+4P+1=2[2P2+2P] =2Q+1
WHERE Q=2P2+2P IS AN INTEGER...HENCE THIS IS ODDNUMBER.
(c) (n-1)2 is even.......TRUE
=[2P+1-1]2=4P2=2[2P2]=2R...EVEN
WHERE
R=[2P2] IS AN INTEGER
(d) (n+1)2 is even....TRUE
=[2P+1+1]2=[2(P+1)]2=4[P+1]2=2[2(P+1)2]=2S=EVEN....
WHERE S=[2(P+1)2] IS AN INTEGER
Please, I need complete detail of this proof of each step.Thank you
HENCE THEY ARE ALL EQUIVALENT STATEMENTS