Order 8 of the following sentences so that they form a logical proof by contradi

Question

Order 8 of the following sentences so that they form a logical proof by contradiction of the statement: If the sum of two integers is even then they have the same parity Choose from these sentences: Your Proof: Assume + y even implies and y have the same parity. Hence r and y have the same parity Parity is not knowable without a paring knife Presume the provided statement is false + y is odd Let x and y be integers with the same parity but with an odd sum. Without loss of generality, assume r is odd and y is even is even and y is odd or z is odd and y is even a +y 2k +1 + 2j 2(k +j) +1 Let x and y be opposite parity integers with even sum. 3k,j E Z such that c - 2k+1 and

Explanation / Answer

Let x and y be opposite parity integers with even sum. x is even and y is odd or x is odd and y is even. without loss of generality assume x is odd and y is even x+y=2k+1+2j=2(k+j)+1 x+y is odd Hence x and y are of the same parity

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