True or false and why? An antisymmetric relation is a relation that is not symme

Question

True or false and why?

An antisymmetric relation is a relation that is not symmetric. Equivalent propositional statements have the same truth values for every truth value assignment to the component statements. An Euler cycle is also a Hamilton cycle. The sentence xP(x, y). y is a free variable. The sentence xP(x, y) has a truth value The sentence x( yP(x, y)), has a truth value. The inductive conclusion for an inductive proof for a sequence of sentences P(n), n = 1,2,3... is n. P(n) is a true statement. In the statement of the theorem "twice an odd integer is even" an existential quantifier is understood.

Explanation / Answer

1 , 2 , 4 , 6 , 7 - true 3 , 5 , 8 - false as far as i know

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