Unformatted text preview: a + b √ 2 + c √ 3 = 0 . Prove that a = b = c = 0. (b) Let a, b, c, d be rational and a + √ b = c + √ d. Prove that either a = c and b = d or b and d are squares of rationals. (c) Let a, b, c, d be rational and x be irrational. In what circumstances is ax + b cx + d rational? 6. Using the axioms of real numbers show that (a) ( ∀ a ∈ R )( ∀ b ∈ R )( ∀ c ∈ R )[(( ac = ab ) ∧ ( a 6 = 0)) = ⇒ ( b = c )]; (b) ( ∀ a ∈ R )( ∀ b ∈ R )[(a )(b ) = ab ]; (c) ( ∀ a ∈ R )( ∀ b ∈ R )( ∀ c ∈ R )[(( a > b ) ∧ ( c < 0)) = ⇒ ( ac < bc )]....
View
Full Document
 Winter '10
 Spyros
 Prime number, Rational number

Click to edit the document details