Indicate which of the following statements are true and which are false. Justify your answers as best you can.
a. ∀x ∈ Z+, ∃y ∈ Z+ such that x = y + 1.
b. ∀x ∈ Z, ∃y ∈ Z such that x = y + 1.
c. ∃x ∈ R such that ∀y ∈ R, x = y + 1.
d. ∀x ∈ R+, ∃y ∈ R+ such that xy = 1.
e. ∀x ∈ R, ∃y ∈ R such that xy = 1.
f. ∀x ∈ Z+ and ∀y ∈ Z+, ∃z ∈ Z+ such that z = x − y.
g. ∀x ∈ Z and ∀y ∈ Z, ∃z ∈ Z such that z = x − y.
h. ∃u ∈ R+ such that ∀v ∈ R+, uv
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