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ArbitrLikvidat [17]
3 years ago
11

Prove using the notion of without loss of generality that 5x 5y is an odd integer when x and y are integers of opposite parity.

Mathematics
1 answer:
kap26 [50]3 years ago
6 0
The expression is
5x + 5y
We are to prove that it is an odd integer when x and y are integers of opposite parity
First, we can assume
x = 2a (even)
y = 2b + 1(odd)
subsituting
10(a + b) + 5
5 [(2(a + b) + 1]
The term
2(a + b) + 1 is odd and the result of an odd number multiplied by an odd number is odd
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