Question

Write a half-sister relation in propositional calculus for Mary and Ann, where Mary's mother is Sue and her father is Ed and Ann's mother is Sue and her father is Sam.

Answer 1

To express the half-sister relationship between Mary and Ann in propositional calculus, we define that they share one parent (Sue) and have different fathers (Ed for Mary and Sam for Ann), using logical operators.

Step-by-step explanation:

To represent the half-sister relationship between Mary and Ann using propositional calculus, we can define logical statements based on their parental relationships. Mary and Ann are half-sisters if they share one parent but have different parents as the other half of their biological lineage.

Let M be 'Mary', A be 'Ann', S be 'Sue', Ed be 'Ed', and Sam be 'Sam'. We can write the propositional variables as follows:

• Mother of Mary is Sue: M_S
• Father of Mary is Ed: M_Ed
• Mother of Ann is Sue: A_S
• Father of Ann is Sam: A_Sam

We use logical conjunction (AND) and logical disjunction (OR) to express the relationship:

Mary and Ann are half-sisters if and only if they share one parent and have different second parents: (M_S AND A_S) AND ((NOT M_Ed AND A_Sam) OR (NOT A_Sam AND M_Ed)).