Logic Unit 2:
Symbolization Answers
©2011
Niko Scharer
1
UNIT 2
SENTENTIAL LOGIC:
SYMBOLIZATION
Answers to Exercises
2.4 E1
UNDERSTANDING THE MATERIAL CONDITIONAL…
A LITTLE LOGIC PUZZLE:
Discussion & Answers
Every card has a number on one side and a letter on the other.
Suppose there is a rule:
If one side of a card has an odd number on it, then the other side has a vowel on it.
Which of the following cards must you turn over in order to test whether the rule was broken?
11
20
B
E
You need to turn over the 11 (to make sure the other side has a vowel on it) AND
you must
turn over the B (to make sure that the other side doesn’t have an odd number on it.)
We test
the affirmation of the antecedent (11) and the denial of the consequent (B)
Now consider the following rule:
If one side has a consonant on it, the other side has an
even number on it.
We turn over the same two cards to test it!
(11 and B) The two rules are
equivalent.
The antecedent of the second rule is the negation of the consequent of the first rule, and the
consequent is the negation of the antecedent.
P
Q
is logically equivalent to ~Q
~P.
If you have a true antecedent, you need to check if the consequent is true as well
–
if not, the
conditional is false and the rule is broken!
If you have a false consequent, check if the
antecedent is false as well
–
if not, the conditional is false and the rule is broken.
Now consider this rule:
A person can drink alcohol only if he/she is 19 years or older.
Each of the following people is drinking a beverage.
Which of the following people must you
learn more about in order to determine whether the rule was broken?
Adam:
age 23
Betty:
age 17
Carol:
drinking
soda
Darren:
drinking
beer
In this case, we have to learn more about Betty (what she is drinking) and more about Darren
(how old he is.)
Again, we test the affirmation of the antecedent (those drinking alcohol) and
the negation of the consequent (under 19 years old.)
This rule is logically equivalent to:
If a person is drinking alcohol then he/she must be 19 years or older.
If a person is not 19 years or older, then he/she must not drink alcohol.

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