## Exam Information

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## Sample Document Text

250, practice exam-I
1. Is
q
ceilingleft2ceilingright <
l ?
2
m
? EXPLAIN.
2. What is P4i=1ceilingleft(i+10)/(i+1)ceilingright? (note- each term has a ceiling.)
3. For each of the following arguments, either (1) write valid and show it is valid
using only the rules of logic on the sheet (which are at the back of the exam),
or (2) Write not valid and show why using rows of a truth table.
(a)
p1 : p1 ? p2
p2 : p2 ? p3
p3 : p3 ? p4
p4 : p4 ? p5
p5 : p5 ? p6
p6 : p6 ? p7
p7 : p7 ? p1
conclusion : p2 ? p1
(b)
p1 : p1 ?p2 ?¬p3
p2 : ¬p1 ?p3
p3 : p3 ? p1
conclusion ¬p1 ?¬p2
4. For this problem the symbols ?, ?, and || (the absolute value sign) have their
usual meaning. for the sentence below, give (1) a non-empty domain where the
sentence is true, and (2) a non-empty domain where the sentence is false. all
domains given should be subsets of r (the reals). Justify your answers (one brief
sentence each).
(?z)(?x)(?y)[|x?y|? z].
5. Prove the following.
(a) for all naturals x, if x5 ? 0 (...

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