2
Answer:
p
q
T
T
F
F
T
F
T
F
pVq
(p V q)  ~p
~p
T
T
T
F
F
F
T
T
F
F
T
T
Answer: p  q
p
q
~q
T
T
F
F
T
F
T
F
F
T
F
T
(qVp)  ~q
(qVp)
T
T
T
F
F
T
F
T
P
q
r
~p
~q
T
T
F
F
F
~q V r
F
~p  (~q V r)
T
6.Determine which, if any, of the three statements are equivalent.
I) If the pipe is leaking, then I will not call the roofer.
II) It is not the case that the pipe is leaking and I will call the roofer.
III) Either the pipe is not leaking or I will not call the roofer.
A.
B.
C.
D.
E.
I and II are equivalent
II and III are equivalent
I and III are equivalent
I, II, and III are equivalent
None are equivalent
7. Write the argument below in symbols to determine whether it is valid or invalid.
State a reason for your conclusion. Specify the p and q you used.
P= the gazebo is made of wood
Q= the vine is growing on the gazebo
We want to know if ((pVq)~p) q is valid
P
q
((pVq)~p) q
T
T
T
T
F
T
F
T
T
F
F
T
Yes is valid.
8. Determine which, if any, of the three statements are equivalent. Give a reason
for your conclusion. Show complete work and submit your solution to the week 3,
assignment 3 dropbox.
I) If the cat does not have claws, then the cat cannot scratch the furniture.
II) If the cat can scratch the furniture, then the cat has claws.
III) If the cat has claws, then the cat can scratch the furniture.
a.
b.
c.
d.
e.
I and II are equivalent
I and III are equivalent
II and III are equivalent
I, II, and III are equivalent
None are equivalent
9. Create an Euler diagram to determine whether the syllogism is valid or invalid.
M = monkeys
L = Animals that eat lizards
Since Koko does not eat lizards koko can belong to M or not
Answer: is not valid
10. If the argument below is valid, name which of the four valid forms of argument
is represented. If it is not valid, name the fallacy that is represented.
If Sally is on vacation, then Tom is at work.
Sally is not on vacation.
Therefore, Tom is not at work.
Answer; fallacy : denying the antecedent
11.Form the inverse: If I do not mow the lawn, then the grass grows too tall.
A. If the grass grows too tall, then I did not mow the lawn.
B. If I mow the lawn, then the grass does not grow too tall.
C. If the grass does not grow too tall, then I mowed the lawn.
D. If the grass does not grow too tall, then I did not mow the lawn.
E. If the grass grows too tall, then I mowed the lawn.
12. Write the compound statement in symbols.
Let r = The food is good, p = I eat too much, q = I'll exercise.
I'll exercise if I don't eat too much.
Answer: the first option (~pq)
13. Construct a truth table for ~(~q V p)
P
T
T
F
F
q
T
F
T
F
~q
F
T
F
T
~qVp
T
T
F
T
~(~qVp)
F
F
T
F