Question

Let D be the domain of 8-bit signed binary numbers, not mathematical integers.

Is the following statement true?

∀x ∈ D, ∀y ∈ D, ((x > 0) ^ (y > 0)) → (x + y) > 0

Hint: bear in mind that the + here is addition over 8-bit signed binary numbers (clock arithmetic), NOT standard mathematical addition.

Group of answer choices

A. Definitely true.

B. Definitely false.

C. As is, can't tell, but I could tell with further information.

D. It's impossible to tell.

E. The statement is ill-formed.

Answer 1

--> Let's see the statement again:

∀x ∈ D, ∀y ∈ D, ((x > 0) ^ (y > 0)) → (x + y) > 0

--> We, will prove this false by taking an example:

Let x = 01111111 , y = 00000001

--> x and y are positive. Let's see x+y

                  01111111

                  00000001

                 ----------------

                  10000000

--> The output 10000000 is equal to -128 which is negative.

--> So, the statement is Definitely false.

--> Hence the answer is option B)