CMSC 250 Homework 1 Fall 2001

Due Wed Sept 5 at the beginning of your discussion section.

1. Translate the following to logical expressions assuming:
   • p = ``Pete went to the store.''

   • r = ``Rose went to the store.''

   • q = ``Quincey went to the store.''

   1. Pete and Quincey went to the store.

   2. Quincey went to the store with Pete or Rose.

2. Determine which of the following are statements and which are not.
   1. The sun will rise tomorrow.

   2. Is this sentence a statement?

   3. This sentence is not a statement.

   4. Sparkly Cola is the best.

3. For each of the following, translate the logical expression to an English statement and then give values which would make the statement true. Assuming the following variables:
   • p = ``n is less than 6.''

   • r = ``n is greater than 2.''

   • q = ``n is not equal to 4.''

   1. $(p\wedge q)\wedge r$

   2. $(p\vee q)\wedge \sim r$

   3. $p\wedge \sim q$

4. Write the truth table for the following statement: $p\,\wedge \sim p$.

5. Write the truth table for the following statement: $(p\, \wedge \sim q)\vee (\sim p \wedge q)$.

6. Show that the statement `` $p\wedge q\vee r$'' is ambiguous by writing the truth tables for $(p\wedge q)\vee r$ and $p\wedge (q\vee r)$ and showing that they are not equal.

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