Let S(x) be the predicate "x is a student",T(x) be the predicate "x is a teacher"and Q(x,y) be the predicate "x has asked y a question" where the domain consists of all people associated with the school. Use quantifiers to express the statement.
"Some student has never been asked a question by a Teacher"
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A
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∃x(S(x) ∨ ∀y(T(y)) → ¬ Q(x,y))) |
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B
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¬∀x(S(x) ∨ ∀y(T(y)) → ¬ Q(y,x))) |
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∃x(S(x) ∧ ∀y(T(y)) → ¬ Q(y,x))) |
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¬∀x(S(x) ∧ ∀y(T(y)) → Q(x,y))) |
All options seems to be wrong to me. But the last one looked closest. Can anyone pls help me in understanding this?
What I am up to –
As far as i know, with ∃, we always use ‘^’ and with ∀ we use ‘→ ’.
So, The statement would be translated as-
∃x∀y S(x) ∧ T(y) ∧ ¬Q(y,x)
=> ∃x∀y ¬( ¬( S(x) ∧ T(y) ) ∨ Q(y,x) )
=> ¬ ∀x∃y ( ( S(x) ∧ T(y) ) → Q(y,x) ) [ ¬P v Q = P→Q ]
None of the options are matching….
