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1. True or false: The two propositions
∃ x ∈ N . ∀ y ∈ N . P(x,y)
∀ y ∈ N . ∃ x ∈ N . P(x,y)
If you think this is true, give a brief explanation.
If you think this is false, give an example of P(x,y)
for which the two propositions are not equivalent.