A. Notes
Boolean expressions such as !A && !(B && !C) are called compound boolean expressions since !, && or || are used to connect multiple boolean variables.
We can build a truth table to find out what ordered pairs or triples will make a compound boolean expression true (or false).
When evaluating a compound boolean expression, it's a good practice to evaluate one part at a time.
B. HWs
1. What ordered pair(s) will make the following boolean expressions false?
A || ! B
!(A&&B) || A
2. What ordered triple(s) will make the following boolean expressions true?
!A || !B || !C
!(A || B || C)
!(A && B && C)
3. Assume that both a and b are integers. Will "a > b and b < 0" make the following boolean expression always true?
!(a <= b) && (a * b > 0)
4. Given that a, b, and c are integers, consider the boolean expression
(a < b) || !((c == a * b) && (c < a))
which of the following will guarantee that the expression is true?
(A) c < a is false.
(B) c < a is true.
(C) a < b is false.
(D) c == a * b is true.
(E) c == a * b is true, and c < a is true.
1. A=0, B=1 A=1, B=1 A=0, B=0
2. A=1, B=1
3. A=0, B=0, C=0 A=1, B=0, C=0 A=1, B=1, C=0 A=1, B=0, C=1 A=0, B=1, C=0 A=0, B=1, C=1 A=0, B=0, C=1
4. [A=1, B=0, C=0], [A=1, B=1, C=0], [A=1, B=0, C=1], [A=0, B=1, C=0], [A=0, B=1, C=1], [A=0, B=0, C=1], [A=1, B=1, C=1]
5. A=1, B=1, C=1
6. yes
7. B