Part IV (15 points). a) Write the negation, the contrapositive, the converse of the following: For a prime number
p
and
kinZ^(+)
, if 4 divides
p-1
, then
p
can be written as the sum of
k
squares. Negation: Contrapositive: Converse: b) State the negation of the following statements (i) For every rational number
r
, the number
(1)/(r)
is rational. (ii) There exists a rational number
r
such that
r^(2)=2
c) Prove that an integer is odd if and only if its square is odd.

Question

Part IV (15 points). a) Write the negation, the contrapositive, the converse of the following: For a prime number

p

and

kinZ^(+)

, if 4 divides

p-1

, then

p

can be written as the sum of

k

squares. Negation: Contrapositive: Converse: b) State the negation of the following statements (i) For every rational number

r

, the number

(1)/(r)

is rational. (ii) There exists a rational number

r

such that

r^(2)=2

c) Prove that an integer is odd if and only if its square is odd.

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Expert Answer to -  Part IV (15 points). a) Write the negation, the contrapositive, the converse of the following: For

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Solution for -  Part IV (15 points). a) Write the negation, the contrapositive, the converse of the following: For

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This an additional answer to -  Part IV (15 points). a) Write the negation, the contrapositive, the converse of the following: For

(Solved): Part IV (15 points). a) Write the negation, the contrapositive, the converse of the following: For ...