This is a reviewer on Discrete Mathematics with topics:
Conditional Proof of Validity, Validation of Arguments.
I. Determine if the following are valid or invalid arguments: (2 Points Each)
Invalid 1)Ann goes whenever I go. Ann goes. Therefore I go.
Valid 2)Joey stays whenever May stays. Joey didn't stay. So May didn't stay.
Invalid 3)Bill reads the news. John also reads the news. So Bill or John reads the news.
Invalid 4)Jake runs. That is why Jake runs and Jill walks.
Valid 5)Mr. See and Mr. Lim play golf. Therefore Mr. See plays golf.
II. Show that - ( p -> ( p-> q ) ) is equivalent to p ^ - q by rules of replacement. ( 5 Points )
III. Show that - \/x ( P(x) v -Q(x) ) is equivalent to 3x ( -P(x) ^ Q(x) ) by rules of replacements ( 5 Points )
IV. Prove each of the following arguments:
1. You will write a correct program if and only if you follow the procedures. If you follow the procedures then you are conventional. You are not conventional and you are always successful. If you are always successful then you will write a correct program. So you will write a correct program. (W, P, C, S)
2. All even numbers are rational and are divisible by two. Some even numbers are divisible by four. Hence some numbers are divisible by two and by four. (Ex, Rx, Tx, Fx)
I. Determine if the following are valid or invalid arguments: (2 Points Each)
Invalid 1)Ann goes whenever I go. Ann goes. Therefore I go.
Valid 2)Joey stays whenever May stays. Joey didn't stay. So May didn't stay.
Invalid 3)Bill reads the news. John also reads the news. So Bill or John reads the news.
Invalid 4)Jake runs. That is why Jake runs and Jill walks.
Valid 5)Mr. See and Mr. Lim play golf. Therefore Mr. See plays golf.
II. Show that - ( p -> ( p-> q ) ) is equivalent to p ^ - q by rules of replacement. ( 5 Points )
III. Show that - \/x ( P(x) v -Q(x) ) is equivalent to 3x ( -P(x) ^ Q(x) ) by rules of replacements ( 5 Points )
IV. Prove each of the following arguments:
1. You will write a correct program if and only if you follow the procedures. If you follow the procedures then you are conventional. You are not conventional and you are always successful. If you are always successful then you will write a correct program. So you will write a correct program. (W, P, C, S)
2. All even numbers are rational and are divisible by two. Some even numbers are divisible by four. Hence some numbers are divisible by two and by four. (Ex, Rx, Tx, Fx)
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