Statistics

1 . Consider the following logical equivalences:

1 Show that OR is an associative operator on propositions, that is, (�P�+�Q�)�+�R�
 is logically equivalent to P�+�(�Q�+�R�)�
.

2 Show that P�→�Q�
 is logically equivalent to (�∼�P�)�+�Q�
. Use this to write P�↔�Q�
 only in terms of NOT and OR operations.

2 . (Lewis Carroll) Suppose we are given the premises:

1 "All babies are illogical." 2 "Nobody who can manage a crocodile is despised." 3 "Illogical people are despised."

What can we conclude about babies? Prove your claim using the rules of deduction. Is this a true claim, a valid deduction, or both?