Boolean Algebra

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Show your work for each problem.

1.
Which law says $A \land \neg A = 0$ ?
1. a)Complement law
2. b)Idempotent law
3. c)Absorption law
4. d)Identity law
2.
What is $A \lor 1$ , whatever the value of $A$ ? Enter 1 for true or 0 for false.
3.
Simplify $(A \lor 0) \land (B \lor 1)$ and check two rows.
4.
$A \lor A$ simplifies to:
1. a) $2A$
2. b) $A$
3. c) $\neg A$
4. d) $A^2$
5.
Simplify $\neg\neg A \land 0$ . The result is a constant: enter 0 or 1.
6.
Check De Morgan's law $\neg(A \land B) = \neg A \lor \neg B$ for $A = 1$ and $B = 0$ .
7.
Which expression is equivalent to $\neg(A \lor B)$ ?
1. a) $\neg A \land \neg B$
2. b) $A \land B$
3. c) $\neg A \lor \neg B$
4. d) $\neg A \lor B$
8.
Which expression equals $A \lor (B \land C)$ ?
1. a) $A \land (B \lor C)$
2. b) $(A \lor B) \land C$
3. c) $(A \lor B) \land (A \lor C)$
4. d) $(A \land B) \lor (A \land C)$
9.
What is the value of $\neg(A \land \neg B)$ for $A = 1$ and $B = 0$ ? Enter 0 or 1.
10.
$(A \land B) \lor (A \land \neg B)$ simplifies to $A$ . Counting one gate for each $\land$ , $\lor$ and $\neg$ , how many gates does the simplification save?
11.
Check the absorption law $A \land (A \lor B) = A$ row by row.
12.
Simplify $(A \lor B) \land (A \lor \neg B)$ and check it.
13.
Simplify $\neg(A \lor \neg B)$ with De Morgan's law.
14.
Which expression is NOT equivalent to $A$ ?
1. a) $(A \lor B) \land (A \lor \neg B)$
2. b) $A \lor (A \land B)$
3. c) $A \land (A \lor B)$
4. d) $A \lor (\neg A \land B)$
15.
In how many of the 4 rows is $(A \lor B) \land (A \lor \neg B) \land (\neg A \lor B)$ true?
16.
Simplify $\neg(A \land B) \land (A \lor \neg B)$ and count the gates saved.
17.
Simplify $A \lor (\neg A \land B)$ .
18.
Simplify $(A \land B) \lor (A \land \neg B \land C)$ and count its true rows.