language, proof and logic,
please proof it
∃x ( ¬A(x) ∨ B(x))
∀x (A(x) ↔ ¬B(x))
∃x ¬A(x)
Answer:
The first statement is "For some x , A(x) implies B(x)" i.e negation of A(x) OR B(x).
(A(x) -> B(x)) =(~A(x) OR B(x))
The second statement is "For all x A(x) is biconditional to negation of B(x)"
(A(x) <-> B(x)) =( (A(x) -> B(x) AND B(x) -> (A(x) )
The third statement is "For some x , Value of A(x) is negative".
language, proof and logic, please proof it ∃x ( ¬A(x) ∨ B(x)) ∀x (A(x) ↔ ¬B(x)) ∃x ¬A(x)
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