The OR Operation

Show your work for each problem.

1.
What is the result of T OR F?
1. a)False
2. b)Cannot be determined
3. c)Error
4. d)True
Answer: True
T OR F = T. Since one input (T) is True, the OR operation returns True.
2.
What is the result of F OR F?
1. a)True
2. b)Both
3. c)False
4. d)Undefined
Answer: False
F OR F = F. OR only returns False when ALL inputs are False. Here both are False, so the result is False.
3.
What is T OR T?
1. a)Invalid
2. b)False
3. c)True
4. d)Extra True
Answer: True
T OR T = T. When both inputs are True, OR returns True. There's no 'extra true' in Boolean logic - the result is simply True.
4.
Complete: F OR T = _____ (answer T or F)
Answer: T
F OR T = T. Since T (True) is one of the inputs, the OR operation returns True.
5.
How many rows in the OR truth table have a True result? (answer with a number)
Answer: 3
3 rows. T OR T = T, T OR F = T, F OR T = T. Only F OR F = F. So 3 out of 4 rows return True.
6.
Evaluate: (5 > 3) OR (2 > 8)
1. a)True
2. b)False
3. c)Both False
4. d)Undefined
Answer: True
(5 > 3) is True, (2 > 8) is False. T OR F = T. One True is enough for OR to return True.
7.
An alarm triggers if: smoke detected OR button pressed. There is no smoke and no one pressed the button. What happens?
1. a)Alarm triggers
2. b)Error in system
3. c)Cannot determine
4. d)Alarm does NOT trigger
Answer: Alarm does NOT trigger
Smoke = False, Button = False. F OR F = F. The alarm does NOT trigger because neither condition is met.
8.
Evaluate: T OR F OR F (answer T or F)
Answer: T
T OR F OR F = T. Since there's one True input, the entire OR chain evaluates to True.
9.
Evaluate: F OR F OR F (answer T or F)
Answer: F
F OR F OR F = F. All inputs are False, so the result is False. This is the only way OR returns False.
10.
You get free dessert if: it's your birthday OR you have a coupon. Today is your birthday but you don't have a coupon. Do you get free dessert?
Answer: Yes
1. Is it your birthday? (answer yes or no) yes
2. So what is the value of B (birthday)? (T or F) T
3. Do you have a coupon? (answer yes or no) no
4. So what is the value of C (coupon)? (T or F) F
5. What is B OR C? (T or F) T
11.
Evaluate: (4 = 4) OR (10 < 5)
Answer: T
1. Is 4 = 4? (T or F) T
2. Is 10 < 5? (T or F) F
3. What is T OR F? T
12.
Evaluate: (T AND F) OR (F OR T)
1. a)Error
2. b)False
3. c)Both
4. d)True
Answer: True
(T AND F) = F, (F OR T) = T. Now: F OR T = T. The final answer is True.
13.
A scholarship requires: GPA > 3.5 OR volunteer hours > 100 OR special talent. Sam has GPA 3.2, 50 volunteer hours, but plays piano professionally. Does Sam qualify?
1. a)No, Sam does not qualify
2. b)Yes, Sam qualifies
3. c)Only partially qualifies
4. d)Need more information
Answer: Yes, Sam qualifies
GPA > 3.5? F (3.2 < 3.5). Hours > 100? F (50 < 100). Talent? T (professional pianist). F OR F OR T = T. Yes, Sam qualifies!
14.
Evaluate: (T OR F) AND (F OR T) AND (T OR T)
Answer: T
1. What is T OR F? T
2. What is F OR T? T
3. What is T OR T? T
4. Now we have T AND T AND T. What is this? T
15.
A video game unlocks a bonus level if: player has 1000 coins OR player has defeated the boss OR player has played 10 hours. Alex has 500 coins, has NOT defeated the boss, but has played 12 hours. Does Alex unlock the bonus?
Answer: Yes
1. Does Alex have 1000 coins? (yes or no) no
2. So C (coins >= 1000) is? (T or F) F
3. Has Alex defeated the boss? (yes or no) no
4. So B (boss defeated) is? (T or F) F
5. Has Alex played 10+ hours? (yes or no) yes
6. So H (hours >= 10) is? (T or F) T
7. What is F OR F OR T? T
16.
If A OR B = True and A = False, what must B be? (answer T or F)
Answer: T
If A = F and A OR B = T, then F OR B = T. The only way this works is if B = T. F OR T = T.