M3210-1 First Homework Assignment

MATH 3210 § 1 FIRST HOMEWORK ASSIGNMENT Due Friday,

A. Treibergs August 29, 2008.

MATH 3210 § 1	FIRST HOMEWORK ASSIGNMENT	Due Friday,
A. Treibergs		August 29, 2008.

Read Anne Roberts' "M3210 Supplemental Notes: Basic Logic Concepts" and Arthur Mattuck's "Introduction to Analysis", Appendices A-B.

Please hand in the following problems.

A. Construct a truth table for the following statement.
      [ P ∧ ( P ⇒ Q ) ] ⇒ Q.

B. Verify using truth tables that
      [ P ∧ ( Q ∨ R ) ]
    is equivalent to
      [ (P ∧ Q ) ∨ (P ∧ R) ].

C. Determine the truth value of each statement assuming that x, y, z are real numbers.

( ∃ x ) ( ∀ y ) ( ∃ z ) ( x + y = z ) ;

( ∃ x ) ( ∀ y ) ( ∀ z ) ( x + y = z ) ;

( ∀ x ) ( ∀ y ) ( ∃ z ) [ ( z > y ) ⇒ ( z > x + y ) ] ;

( ∀ x ) ( ∃ y ) ( ∀ z ) [ ( z > y ) ⇒ ( z > x + y ) ] .

D. Write formally, with quantifiers in the right order. Negate the sentence and interpret.
"Everybody doesn't like something but nobody doesn't like Sara Lee."

Read Anne Roberts' "M3210 Supplemental Notes: Basic Logic Concepts" and Arthur Mattuck's "Introduction to Analysis", Appendices A-B.
Please hand in the following problems. A. Construct a truth table for the following statement. [ P ∧ ( P ⇒ Q ) ] ⇒ Q. B. Verify using truth tables that [ P ∧ ( Q ∨ R ) ] is equivalent to [ (P ∧ Q ) ∨ (P ∧ R) ]. C. Determine the truth value of each statement assuming that x, y, z are real numbers. ( ∃ x ) ( ∀ y ) ( ∃ z ) ( x + y = z ) ; ( ∃ x ) ( ∀ y ) ( ∀ z ) ( x + y = z ) ; ( ∀ x ) ( ∀ y ) ( ∃ z ) [ ( z > y ) ⇒ ( z > x + y ) ] ; ( ∀ x ) ( ∃ y ) ( ∀ z ) [ ( z > y ) ⇒ ( z > x + y ) ] . D. Write formally, with quantifiers in the right order. Negate the sentence and interpret. `"Everybody doesn't like something but nobody doesn't like Sara Lee."`