Which of the following expressions is TRUE if and only if NOT all three variables a, b, and c have the same value?
My teacher:

This kind of tricky wording is to be expected the AP Exam. The phrase "have the same value" we can take to mean equal. Now, "not all three equal" does not mean "all three different", it means at least one is different. So let's use the test case {a=0, b=0, c=1}

! (a == b || b == c || a == c)

! (0 == 0 || 0 == 1 || 0 == 1)

! (true or false or false)

! (true)

false

a > b || b > c || a > c

0 > 0 || 0 > 1 || 0 > 1

false || false || false

false

a >=b &amp;&amp; b >= c &amp;&amp; c >= a

0 >=0 &amp;&amp; 0 >= 1 &amp;&amp; 1 >= 0

true &amp;&amp; false &amp;&amp; true

false

a != b &amp;&amp; b != c

0 != 0 &amp;&amp; 0 != 1

false &amp;&amp; true

false

0 != 0 || 0 != 1

false || true

true

When you think about it logically, given three things, one of them has to be not equal to one of the other two in order for all three of them to not be the same.

Thus the correct answer is A.