Boolean Expressions

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Show your work for each problem.

1.
In $A \lor B \land \neg C$ (no parentheses), which operation is done first?
1. a)AND ( $\land$ )
2. b)OR ( $\lor$ )
3. c)NOT ( $\neg$ )
4. d)Left to right, so OR
2.
Evaluate $A \land B$ for $A = 1$ and $B = 0$ . Answer 1 for true or 0 for false.
3.
Evaluate $A \lor \neg B$ for $A = 0$ and $B = 0$ . Answer 1 for true or 0 for false.
4.
How many rows does the truth table of an expression with the variables $A$ , $B$ and $C$ have?
1. a)3
2. b)6
3. c)9
4. d)8
5.
Evaluate $A \land \neg B$ for $A = 1$ and $B = 1$ . Answer 1 for true or 0 for false.
6.
Evaluate $\neg A \lor B$ for $A = 0$ and $B = 0$ . Answer 1 for true or 0 for false.
7.
Which expression means the same as $A \lor B \land C$ ?
1. a) $(A \land B) \lor C$
2. b) $(A \lor B) \land C$
3. c) $A \land (B \lor C)$
4. d) $A \lor (B \land C)$
8.
Evaluate $A \lor B \land C$ for $A = 1$ , $B = 1$ , $C = 0$ . Answer 1 for true or 0 for false.
9.
Evaluate $\neg(A \land B) \lor C$ for $A = 1$ , $B = 1$ , $C = 0$ . Answer 1 for true or 0 for false.
10.
Evaluate $\neg A \land B \lor A \land \neg B$ for $A = 1$ and $B = 0$ . Answer 1 for true or 0 for false.
11.
In how many rows of its truth table is $\neg A \land B$ equal to 1?
12.
What is the final column of $A \lor \neg B$ for the rows $AB$ = 00, 01, 10, 11?
1. a)0, 1, 1, 1
2. b)1, 0, 1, 1
3. c)1, 1, 0, 1
4. d)0, 1, 0, 0
13.
Build the truth table of $\neg(A \lor B)$ . In how many rows is it equal to 1?
14.
In how many rows of its truth table is $A \land B \lor C$ equal to 1?
15.
Build the truth table of $A \land (B \lor C)$ . In how many rows is it equal to 1?
16.
Build the truth table of $A \land B \lor A \land \neg B$ . Which expression is equivalent to it?
1. a) $A \land B$
2. b) $A$
3. c) $A \lor B$
4. d) $B$
17.
Compare the truth tables of $A \lor B \land C$ and $(A \lor B) \land C$ . In how many rows do they differ?
18.
Evaluate $\neg(A \land B \lor \neg C)$ for $A = 1$ , $B = 0$ , $C = 1$ . Answer 1 for true or 0 for false.