Which of the following statements are true and which are false. justify your answers. hint: this is a great problem. you need to be particularly careful about the order of the quantifiers (∀ and ∃).
(a) ∃ ∈ ℝ such that ∀ ∈ ℝ 2 + 2 = 9.
(b) ∀ ∈ ℝ, ∃ ∈ ℝ such that 2 < +1.
(c) ∀ ∈ ℤ +, ∃ ∈ ℤ + such that = + 1.
(d) ∀ ∈ ℤ, ∃ ∈ ℤ such that = + 1.
(e) ∃ ∈ ℝ such that ∀ ∈ ℝ, = + 1.
(f) ∀ ∈ ℝ +, ∃ ∈ ℝ + such that = 1.
(g) ∀ ∈ ℝ, ∃ ∈ ℝ such that = 1.
(h) ∀ ∈ ℤ + and ∀ ∈ ℤ +, ∃ ∈ ℤ + such that = −
(i) ∀ ∈ ℤ and ∀ ∈ ℤ, ∃ ∈ ℤ such that = −
(j) ∃ ∈ ℝ + such that ∀ ∈ ℝ +, <
(k) ∀ ∈ ℝ +, ∃ ∈ ℝ + such that <