MC36 -- Relation-Based Structures -- Fall 1998
Assignments for Week 2
Problem Set #2 - html
Reading for Monday, September 21:
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Grimaldi: 2.1
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Pay particular attention to Example 2.2. Express p ->q as an English
sentence. Use this expression to explain why p->q is true when p
is false and q is true (row 2 of Table 2.2)
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How many rows are there in a truth table for a compound statement
made up of two primitive statements? What if there are n primitive
statements?
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What kind of statment is p /\ ~p? p\/~p ?
Practice: Grimaldi: 2.1 #1,3,5,7
Reading for Tuesday, September 22:
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Grimaldi: 2.2
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Focus on showing logical equivalence using "Laws of Logic". Duality
and Substitution Rules are less important.
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What logical equivalences allow us to eliminate the connectives -> and
<=> from compound statements?
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Negation of an implication: express in English without beginning
with the word "not". (Ex. 2.13)
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What are the contrapositive, inverse and converse of the implication p->q?
Which are logically equivalent to p->q?
Practice: Grimaldi: 2.2 #5, 7a, 9
Reading for Thursday, September 24:
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Grimaldi: 2.3 (Things to think about when you are reading the
section)
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This section is a little overwhelming. Focus on understanding how
to demonstrate the validity of an argument. Try not to get bogged
down by all of the names of the rules.
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What does it mean to say that "p logically implies q"?
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How would you show that a rule of inference (say Syllogism) is valid using
a truth table?
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Try 2.3 #5
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Why are the arguments given on p85 invalid?
Reading for Friday, September 25: