Question

“If x+y is an even integer then bothx and y are even integers"Which of the following equations issufficient to show that thestatement above is false?a. -2+2=0b. -2+4=2C. -1+4=3d. 3+1=4e. 4+4=8

Answer 1

The statement says that if the result is even integer (like 2, 4, 6, ...) then x and y also are. If we want to disprove that, we need to look for a even integer that have x and/or y not even integer.

All alternatives but c have even integers as result, but only d show x and y odd integers.

So, "d" clearly disproves the statement, because they show that the sum of two odd integers (1 and 3) results in an even integer (4), which contradicts the statement.