A mix-up in a hospital ward caused a mother with $\mathrm{O}$ and $\mathrm{MN}$ blood types to think that a baby given to her really belonged to someone else. Tests in the hospital showed that the doubting mother was able to taste PTC (see problem 9). The baby given to her had O and MN blood types and had no reaction when the bitter PTC chemical was placed on its tongue. The mother had four other children with the following blood types and tasting abilities for PTC:1. type $A$ and $MN$ blood, taster2. type $B$ and $N$ blood, nontaster3. type A and M blood, taster4. type $A$ and $N$ blood, tasterWithout knowing the father's blood types and tasting ability, can you determine whether the child is really hers? (Assume that all her children have the same father.)

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