Question

Boolean evaluation: The two expressions below are logically equivalent. Give a set of values for x, y and z when both boolean expressions produce a result of TRUE.

• Expression 1: (! ((x % 2 == 0) && (y > z)))

• Expression 2: (! (x % 2 == 0) || !(y > z))

I am unsure how to do this- can I get an explanation?

Answer 1

x is odd, and y and z values does not matter.
if this condition satisfies then these expressions always gives a result of TRUE

example:
-----------
x = 7, y = 2, z = 3

1)
(!((x % 2 == 0) && (y > z)))
=>  (!((3 % 2 == 0) && (2 > 3)))
=>  (!((false) && (false)))
=>  !(false)
=>  true

2)
(!(x % 2 == 0) || !(y > z))
=>  (!(7 % 2 == 0) || !(2 > 3))
=>  (!(false) || !(false))
=>  true || true
=>  true