Handout #39
CS103
May 3, 2010
Robert Plummer
CS103 Review Session Problems
Here are the problems from the review sessions over the weekend.
Solutions are in the
next handout.
That is Handout #40.
Note that on the handout, the heading is incorrect,
but the solutions are to the right problems.
1.
Logic Proof (20 points)
Give a proof for the following.
Use numbered steps and refer to those numbers in the
justification you give for each step.
You
are allowed to use De Morgan's laws freely,
both the quantified and unquantified versions
, but cite them as justification if you do.
You will find useful tables at the end of the exam.
Cite named rules, or just the table and
line number if the rule is not named (e.g., Table 7, line 3).
1.
¬
∃
x (R(x)
∧
S(x))
2.
∀
y (S(y)
∨
M(y)
∨
L(y))
∀
x (R(x)
→
(L(x)
∨
M(x)))
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2.
Translations (20 points)
Translate each of the following sentences into firstorder logic.
You may use
only
the following predicates:
I(x)
x is an integer
R(x)
x is rational
x > y
x is greater than y
x = y
x equals y
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 Fall '09
 Equivalence relation, Leland Stanford

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