Discrete Structures207810 marksmathematical Induction
Prove that for all integers x and y, if x2 + y2 is even then x + y is even. Using induction prove that 13 + 23 + 33 + ... + n3 = n2(n + 1)2/4
Prove that for all integers x and y, if $x^2 + y^2$ is even then x + y is even. Using induction prove that $1^3 + 2^3 + 3^3 + ... + n^3 = n^2(n + 1)^2/4$ [10]
The contrapositive of "if x² + y² is even, then x + y is even" is: If x + y is odd, then x² + y² is odd. We prove the contrapositive. This is a valid approach because a statement and its contrapositive are logically equivalent. --- Assume x + y is odd. For the sum of two integers to be odd, one m...