Introduction to Boolean Logic

Show your work for each problem.

1.
In Boolean logic, how many possible values are there?
1. a)Unlimited
2. b)3
3. c)2
4. d)1
Answer: 1
Boolean logic has exactly 2 values: TRUE (1) and FALSE (0). This binary system is the foundation of all computing.
2.
What is TRUE AND TRUE?
1. a)TRUE
2. b)MAYBE
3. c)ERROR
4. d)FALSE
Answer: TRUE
TRUE AND TRUE = TRUE. The AND operator only returns TRUE when both inputs are TRUE. Since both values are TRUE here, the result is TRUE.
3.
What is TRUE AND FALSE?
1. a)MAYBE
2. b)FALSE
3. c)TRUE
4. d)ERROR
Answer: FALSE
TRUE AND FALSE = FALSE. Since AND requires both values to be TRUE, having one FALSE makes the entire expression FALSE.
4.
What is NOT TRUE? Write TRUE or FALSE.
Answer: FALSE
NOT TRUE = FALSE. The NOT operator simply reverses the Boolean value. TRUE becomes FALSE.
5.
What is FALSE OR TRUE? Write TRUE or FALSE.
Answer: TRUE
FALSE OR TRUE = TRUE. The OR operator returns TRUE if at least one input is TRUE. Since we have one TRUE, the result is TRUE.
6.
What is FALSE OR FALSE?
1. a)TRUE
2. b)ERROR
3. c)FALSE
4. d)MAYBE
Answer: FALSE
FALSE OR FALSE = FALSE. OR returns TRUE only if at least one value is TRUE. Since both are FALSE, the result is FALSE.
7.
What is NOT FALSE? Write TRUE or FALSE.
Answer: TRUE
NOT FALSE = TRUE. The NOT operator flips the value. FALSE becomes TRUE.
8.
Evaluate: (TRUE AND FALSE) OR TRUE
Answer: TRUE
1. First, solve the parentheses: TRUE AND FALSE = ? FALSE
2. Now we have: FALSE OR TRUE = ? TRUE
9.
Evaluate: NOT (TRUE OR FALSE)
Answer: FALSE
1. First, solve the parentheses: TRUE OR FALSE = ? TRUE
2. Now apply NOT: NOT TRUE = ? FALSE
10.
Which statement about OR is correct?
1. a)TRUE OR TRUE = TRUE
2. b)OR requires both to be TRUE
3. c)TRUE OR TRUE = FALSE
4. d)OR always returns FALSE
Answer: TRUE OR TRUE = TRUE
TRUE OR TRUE = TRUE. In Boolean logic, OR returns TRUE if at least one input is TRUE. This includes when both are TRUE (called 'inclusive or').
11.
Evaluate: TRUE AND (NOT FALSE)
Answer: TRUE
1. First, solve the parentheses: NOT FALSE = ? TRUE
2. Now we have: TRUE AND TRUE = ? TRUE
12.
Evaluate: (TRUE OR FALSE) AND (NOT TRUE)
Answer: FALSE
1. Solve first parentheses: TRUE OR FALSE = ? TRUE
2. Solve second parentheses: NOT TRUE = ? FALSE
3. Now combine: TRUE AND FALSE = ? FALSE
13.
Evaluate: NOT (FALSE AND FALSE) OR TRUE
Answer: TRUE
1. Solve innermost parentheses: FALSE AND FALSE = ? FALSE
2. Apply NOT: NOT FALSE = ? TRUE
3. Final OR: TRUE OR TRUE = ? TRUE
14.
You need a ticket AND (adult OR accompanied_by_adult) to enter. You have a ticket (TRUE), you're not an adult (FALSE), and you're accompanied by an adult (TRUE). Can you enter?
1. a)Only with extra payment
2. b)Not enough information
3. c)No, I cannot enter
4. d)Yes, I can enter
Answer: Yes, I can enter
ticket AND (adult OR accompanied) = TRUE AND (FALSE OR TRUE) = TRUE AND TRUE = TRUE. You can enter!
15.
Evaluate: (NOT TRUE) AND (NOT FALSE)
Answer: FALSE
1. Solve first NOT: NOT TRUE = ? FALSE
2. Solve second NOT: NOT FALSE = ? TRUE
3. Combine with AND: FALSE AND TRUE = ? FALSE