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.
Some A is not B is equivalent to p ^ ~q.
Determine the validity of the next arguments by using Euler cricles, then transalate the statement into logical statements using the basic connectives, and using truth tables, determine the validity of the arguments. Compare 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
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.
Some A is not B is equivalent to p ^ ~q.
Determine the validity of the next arguments by using Euler cricles, then transalate the statement into logical statements using the basic connectives, and using truth tables, determine the validity of the arguments. Compare 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