5) Which of the following is an equivalence relation? A){ <1,1>, <2,2>,<1,3> } B

Question

5) Which of the following is an equivalence relation?

A){ <1,1>, <2,2>,<1,3> }
B){ <1,1>, <2,2>,<1,3>, <3,1>, <3,3> }
C){ <1,1>, <2,2>,<1,3>, <3,3> }

6)Under what circumstances would this statement be true

(z)(y)[(G(z) & W(y)) E(y,z)]]

Select all that apply.

A)If there are no wolfs.
B)If there is a wolf who has eaten every goat.
C)If every goat was eaten by a wolf.
D)If there are no goats.

7)Under what circumstances would this statement be false

(z)(y)[(G(z) & W(y)) E(y,z)]]

Select all that apply.

A)If there is a goat that was not eaten by a wolf.
B)If there is a wolf that has not eaten a goat.
C)If some goat was eaten by a wolf.
D)If there is a single wolf that has eaten every goat.

Explanation / Answer

5. B){ <1,1>, <2,2>,<1,3>, <3,1>, <3,3> }
Its an equivalence relation because its reflexive, symmetric and transitive

6.B)If there is a wolf who has eaten every goat.
D)If there are no goats.

7) A)If there is a goat that was not eaten by a wolf.
C)If some goat was eaten by a wolf.

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