Q38

MSQ2 marks

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"? The meanings of the predicates used are: mother $(y, x): y$ is the mother of $x$ noteq $(x, y): x$ and $y$ are not equal

(A)

$\forall x \exists y \exists z(\operatorname{mother}(y, x) \wedge \neg \operatorname{mother}(z, x))$

(B)

$\forall x \exists y[\operatorname{mother}(y, x) \wedge \forall z( \operatorname{noteq} (z, y) \rightarrow \neg \operatorname{mother} (z, x))]$

(C)

$\forall x \forall y[\operatorname{mother}(y, x) \rightarrow \exists z( \operatorname{mother} (z, x) \wedge \neg \operatorname{note} q(z, y))]$

(D)

$\forall x \exists y[\operatorname{mother}(y, x) \wedge \neg \exists z( \operatorname{note} q(z, y) \wedge \operatorname{mother} (z, x))]$

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