Practice problems on quantified statements

3. Let f be a function on R. To say that f is uniformly continuous means:for each positive real number ε, there is a positive real number δ such that for alla, b ∈ R, if |a − b| < δ, then |f(a) − f(b)| < ε(a) Write the definition of “f is uniformly continuous” using the quantifiers ∀ and ∃.(b) Write the negation of “f is uniformly continuous” without using quantifiers.4. Let a n be a sequence of real numbers. To say that a n converges to L as n goes toinfinity means:given any positive real number ε, there is a positive integer N such that for alln > N, |a n − L| < ε(a) Write the definition of “a n converges to L” using the quantifiers ∀ and ∃.(b) Write the negation of “a n converges to L” without using quantifiers.