Q4: Equivalence#

Time Estimate15-30 minutes   Grade Impact0.5%   DueSep 21 @ 12pm  

Objective
Reinforce an understanding of Venn diagrams and Karnaugh maps.

Free Response Questions#

1. Why is it important to know if two Boolean circuits or expressions are equivalent?

2. What are some pros and cons of using a Venn diagram versus a Karnaugh map?

3. When is algebraic manipulation more useful than a truth table?

Multiple Choice Questions#

4. Which of the following expressions is represented by the following Venn diagram?

   • $y \land \lnot x$
   • $x \land \lnot y$
   • $y \lor \lnot x$
   • $x \lor \lnot y$

5. Consider the following truth table. What expression represents Out?

   A	B	Out
   0	0	0
   0	1	1
   1	0	1
   1	1	0

   • $A \land B$
   • $A \lor B$
   • $A \oplus B$
   • $A \equiv B$

6. Which of the following is logically equivalent to $(x \land y) \lor (x \land z)$? You may use a truth table, K-map, or Venn diagram.

   • $x \land (y \lor z)$
   • $(x \lor y) \land (x \lor z)$
   • $x \land y \land z$
   • $(x \land y) \land (x \land z)$

7. True or False: If two Venn diagrams are highlighted identically, they represent equivalent expressions.

   • True
   • False
   • Not necessarily true or false

8. True of False: It is possible to draw a Venn diagram with 4 variables.

   • True
   • False
   • Not necessarily true or false

9. Which expression is equivalent to $\lnot(x \land y)$?

   • $\lnot x \land \lnot y$
   • $\lnot x \lor \lnot y$
   • $x \lor y$
   • $x \land \lnot y$

10. Consider this truth table for inputs X, Y, Z:

    X	Y	Z	Out
    0	0	0	0
    0	0	1	0
    0	1	0	0
    0	1	1	1
    1	0	0	1
    1	0	1	1
    1	1	0	1
    1	1	1	1

    Which expression corresponds to this table?

    • $X \lor (Y \land Z)$
    • $(X \lor Y) \land (X \lor Z)$
    • $(X \land Y) \lor (X \land Z)$
    • $Y \land Z$