Let the predicate P(x,y) mean r is a parent of y. You are allowed to use...

 

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Let the predicate P(x,y) mean r is a parent of y. You are allowed to use the quantifiers, the predicates P, =, and +, logical operators and variables, and, in each part, the predicates from the previous parts. For the purposes of the problem below, the notion of "sibling" includes half-siblings. For long formulas, please add English-languages phrases explaining what different parts of the formula are saying, so that graders can understand what you mean. For example, underline a portion of the formula, or separate it on a line by itself, and write next to it "this expresses that a is a cousin or a sibling of b." Hint: it helps to draw genealogical trees. a) Define a predicate G(a, b) which is true when a is a grandparent of b. b) Define a predicate S(a, b) which is true when a is a sibling of b (recall that a person is not their own sibling). Let the predicate P(x,y) mean r is a parent of y. You are allowed to use the quantifiers, the predicates P, =, and +, logical operators and variables, and, in each part, the predicates from the previous parts. For the purposes of the problem below, the notion of "sibling" includes half-siblings. For long formulas, please add English-languages phrases explaining what different parts of the formula are saying, so that graders can understand what you mean. For example, underline a portion of the formula, or separate it on a line by itself, and write next to it "this expresses that a is a cousin or a sibling of b." Hint: it helps to draw genealogical trees. a) Define a predicate G(a, b) which is true when a is a grandparent of b. b) Define a predicate S(a, b) which is true when a is a sibling of b (recall that a person is not their own sibling).

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