Let p be “The object belongs to set A.” Let q be “the object belongs to set B.”
All A is B is equivalent to p ------> q.
No A is B is equivalent to p ----> ~ q.
Some A is B is equivalent to p ^ q.
All A is not B is equivalent to p ^ ~ q.
Determine the validity of the next arguments by using Euler circles, then translate the states into logical statements using the basic connectives, and truth tables, determine the validity of the arguments. Compare and explain your answers.
(a) No A is B.
Some C is A.
Some C is not B.
(b) All B is A.
All C is A.
All C is B.
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