Quantified Statements?

Determine whether the following statement and it's negation are true:

∀x ∈ℝ, ∃y ∈ℝ such that xy=2.

for all x in set of real numbers, there exists y in set of real numbers such that xy=2.

just making sure i'm understanding the symbols right.

not sure where to go from here.

is the question asking if any real number x by static number y would = 2?

1 Answer

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  • 8 years ago
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    The statement is false if the negation is true, namely

    ∃x∈ℝ such that ∀y∈ℝ, xy ╪ 2.

    This negation is true. Let x = 0. There is no real y that yields xy = 2.

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