WeBWorK Standalone Renderer

Consider the following truth table.

p	q	r	f(p,q,r)
0	0	0	1
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	0
1	1	0	0
1	1	1	1

Give a disjunctive normal form to represent $f(p,q,r)$ .

A. $(\neg p \wedge q \wedge r) \vee (p \wedge q \wedge r)$
B. $(\neg p \wedge \neg q \wedge \neg r) \vee (\neg p \wedge q \wedge r)$
C. $(\neg p \wedge \neg q \wedge r) \vee (\neg p \wedge q \wedge \neg r) \vee (p \wedge \neg q \wedge \neg r) \vee (p \wedge \neg q \wedge r) \vee (p \wedge q \wedge \neg r)$
D. $(\neg p \wedge \neg q \wedge \neg r) \vee (\neg p \wedge q \wedge r) \vee (p \wedge q \wedge r)$

Give a conjunctive normal form to represent $f(p,q,r)$ .

A. $(p \vee q \vee \neg r) \wedge (p \vee \neg q \vee r) \wedge (\neg p \vee q \vee r) \wedge (\neg p \vee q \vee \neg r) \wedge (\neg p \vee \neg q \vee r)$
B. $(p \vee \neg q \vee r) \wedge (\neg p \vee q \vee r) \wedge (\neg p \vee q \vee \neg r) \wedge (\neg p \vee \neg q \vee r)$
C. $(\neg p \vee \neg q \vee \neg r) \wedge (\neg p \vee q \vee r) \wedge (p \vee q \vee r)$
D. $(p \vee q \vee \neg r) \wedge (p \vee \neg q \vee r) \wedge (\neg p \vee q \vee r) \wedge (\neg p \vee q \vee \neg r)$

Express $a \vee b$ using only a NOR.

A. NOR(NOR(a,a),NOR(b,b))
B. NOR(NOR(a,b),NOR(a,b))
C. NOR(a,b)
D. NOR(NOR(a,b),NOR(b,b))

Express $a \wedge b$ using only a NAND.

A. NAND(a,b)
B. NAND(NAND(a,a),NAND(b,b))
C. NAND(NAND(b,a),NAND(b,b))
D. NAND(NAND(a,b),NAND(a,b))

You can earn partial credit on this problem.