MA123 Study Guide for Test 1 Chapter 3 (sections 1,2,3,4,5,6)
NEGATION
All Some…. not..
Some No
~ ( p ∧q ) ( ~ p ٧ ~ q )
~ ( p ٧ q ) ( ~ p ∧ ~ q )
Direct Indirect
(Contrapositive
)
Transitive Disjunctive
Reasoning
Fallacy of
Converse
Fallacy
of
Inverse
Misuse of
Transitive
Misuse of
Disjunctive
Reasoning
p
→
q
p
p
→
q
~ q
p
→
q
q → r
p ٧ q
~ p
p
→
q
q
p
→
q
~ p
p
→
q
p → r
p ٧ q
p
∴
q
∴
~ p
∴
p
→
r q
∴
p
∴
~ q
∴
q
→
r ~q
Where appropriate, write in sentences, with proper use of capital letters and punctuation.
1. Let p: Sam worked late q: Sam went fishing. r: Sam went home for the weekend.
Translate into words: A. p ∧ ~q B. ~q → p C. ~ ( p ٧ q ) → p
D. ~ ( p ٧ q ) → (~p ∧ q)
2. Write as an If…. then statement in words : A. All trees have leaves.
B. You will fall over the cliff if you lean on the fence.
C. You will eat enchiladas when you go to Casa Mexicana.
3. Complete a truth table for the following, and tell if it is a tautology.
A. ~ q → ~ p B . ~ ( p ٧ q ) → p C. ~ ( p ٧ q ) → (~p ∧ q)
D. [(p → q) ∧ ~q ] → ~p
4. Let p : Round candy has nuts.
q: Striped candy has cherries
r: Dark candy is bitter.
Translate into symbols each of the following
a. Round candy does not have nuts or striped candy has cherries
b. Dark candy is bitter and striped candy does not have cherries.
c. If dark candy is not bitter and striped candy has cherries, then round candy does not have nuts.
Translate into words using the above definitions of p and q
d. ~ p → q
5. Write the negation of each statement below in words. If the sentence contains a qualifier, write the negation
by changing the qualifier.
a. All authors can read. b. Some authors are wealthy.
c. Some cars do not have air bags. d. The cat is outside.
6 . Which of the following are statements? A. The time is 2:45 pm.
B. Is London in France?
C. Wash your hands.
D. We will go to the beach or to the mountains.
7. Form a valid conclusion using ALL of the given statements.
A. If you do not have money, you will not go to the play.
You go to the play.
B. If you eat Wheaties, you will hit home runs.
If you hit home runs, the Cardinals will hire you.
If the Cardinals hire you, you will move to St. Louis.
C. If a cat cries, he gets fed.
Sam the cat is hungry.
D He is in sports or in speech. He is not in sports.
8. Designate each of the following as valid or invalid.
