Determine which, if any, of the three statements are equivalent.
I) If there are cats in the yard, then there are no birds in the trees.
II) Either there are no cats in the yard or there are no birds in the trees.
III) If are no birds in the trees, then there are no cats in the yard.
(Points : 2)
_ I, II, and III are equivalent
_ I and II are equivalent
_ II and III are equivalent
_ I and III are equivalent
_ None are equivalent
Solution
None are equivalent. This is because for I, having cats in the yard implies no birds
in the tree, but does not remove the possibility that the cats might not be present and there would
still be no birds. II requires one of the kinds of animals, either cats or birds, to be present at all
times, thus not necessarily always being equivalent with I. II and III are not equivalent because
III implies that no birds = no cats, while II says that there must either be birds or cats. I and III
are not equivalent because III negates I, saying that if there are no birds there are no cats, while I
states that if there are cats there will be no birds..
Determine which, if any, of the three statements are equivalent. I.pdf
1. Determine which, if any, of the three statements are equivalent.
I) If there are cats in the yard, then there are no birds in the trees.
II) Either there are no cats in the yard or there are no birds in the trees.
III) If are no birds in the trees, then there are no cats in the yard.
(Points : 2)
_ I, II, and III are equivalent
_ I and II are equivalent
_ II and III are equivalent
_ I and III are equivalent
_ None are equivalent
Solution
None are equivalent. This is because for I, having cats in the yard implies no birds
in the tree, but does not remove the possibility that the cats might not be present and there would
still be no birds. II requires one of the kinds of animals, either cats or birds, to be present at all
times, thus not necessarily always being equivalent with I. II and III are not equivalent because
III implies that no birds = no cats, while II says that there must either be birds or cats. I and III
are not equivalent because III negates I, saying that if there are no birds there are no cats, while I
states that if there are cats there will be no birds.
