Question

1). Let G be the statement: " for all real numbers a and b, if a -|_a_| < 1/2 and b - |_b_| < 1/2 then |_a + b_| = |_a_| + |_b_|"

(the symbol is for the FLOOR of a and b)

A. is G true? prove it

b. state wether the CONVERSE, CONTRAPOSITIVE AND NEGATION ARE TRUE and prove.

Thanks for all your help.

Answer 1

(a-[a]) + (b-[b]) < 1/2 + 1/2 = 1
so, the fractional part of the sum will not cause it to exceed the next integer.

will think on the other parts, but maybe you have some ideas you can post in the meantime.