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I'm having trouble translating several phrases to FOL statements

a. No husband, who gives wife presents can be cross-grained.

b. No husband can failed to be cross-grained, if his wife does not keep him in proper order.

Which I translated to

Setting the Universe of discourse to be husbands

a. $¬∃x\big(GivesPresent(x) ⟹Crossgrained(x) \big)$

b. $¬∃x\big(¬KeepinCheck(x) ⟹¬Crossgrained(x) \big)$

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Translating 'an A is a B' into FOL would give $\exists x(A(x)\land B(x))$. Both of your sentences can be expressed in a way that is analogous to 'an A is (not) a B', so you'll want to use a connective like $\land$ rather than $\to$, possibly changing some negations also.

I'm trying to avoid giving you the answer outright (we learn best when we have to struggle a little), so if you're still confused, ask and I can explain more.

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