Using the following predicates: • B(x) for “x has bifurcated horns” • D(x) for “

ID: 3743110 • Letter: U

Question

Using the following predicates:

• B(x) for “x has bifurcated horns”

• D(x) for “x suffers from dermal asthenia”

• F(x) for “x is female”

• M(x, y) for “x is the mother of y”

• S(x) for “x is Syldavian”

• U(x) for “x is a unicorn”

express the following statements as formulas in first-order predicate logic:

a. Mothers are female

b. A mother of a unicorn is a unicorn

c. All female unicorns with bifurcated horns suffer from dermal asthenia

d. Mother unicorns with dermal asthenia pass the condition on to all their offspring

e. All Syldavian unicorns have bifurcated horns

f. Any unicorn whose mother is Syldavian suffers from dermal asthenia

a. xy (M(x, y) -> F(x))

For all x and y, where x is the mother of y (x is a mother), implies that x is female.

b. xy ((M(x, y) U(y)) -> U(x))

For all x and y, where x is the mother of y, and y is a unicorn, implies that x is a unicorn

c. x ((F(x) U(x) B(x)) -> D(x))

For all x, where x is female and a unicorn and has bifurcated horns, implies that x has dermal asthenia

d. xy ((M(x,y) U(x) D(x)) -> D(y))

For all x and y, where x is the nother of y and x is a unicorn and x has dermal asthenia, implies that y has dermal asthenia

e. x ((S(x) U(x)) -> B(y))

For all x, where x is Syldavian and a unicorn, implies that x has bifurcated horns

f. xy ((M(x,y) U(y) S(x)) -> D(y))

For all x and y, where x is the mother of y and y is a unicorn and x is Syldavian, implies that y has dermal asthenia

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