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## Homework Statement

Are these statements true or false? Prove/reason why/why not.

a.)∃x∈R , ∃y∈R : (x

^{2}-2)

^{2}+y

^{2}=1

b.)∀x∈R , ∀y∈R : y >x

^{2}-1

c.)∀x∈R , ∃y∈R : |x+y|=1

d.)∃x∈R , ∀y∈R :|x|>y

## The Attempt at a Solution

a.) true, for example (x=1 and y=0)

b.) false, because if I choose (x=1 and y=0) I get 0>(1-1) which cannot be true so the statement cannot be always true

c.)false? Let. x=-y+8 ⇒|8|≠1 x can be any real number

d.)?