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.
--> 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)
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