Prove using the notion of without any loss of generality that 5x+5y is odd when x and y are integers of opposite polarity Solution 5x+5y = 5(x+y) if x is even and y is odd then x+y is odd and 5(x+y) will be odd if y is even and x is odd then x+y is odd and 5(x+y) will be odd Hence 5x+5y is odd when x and y are integers of opposite polarity.

1. Prove using the notion of without any loss of generality that 5x+5y is odd when x and y are
integers of opposite polarity
Solution
5x+5y = 5(x+y) if x is even and y is odd then x+y is odd and 5(x+y) will be odd if
y is even and x is odd then x+y is odd and 5(x+y) will be odd Hence 5x+5y is odd when x and y
are integers of opposite polarity