We are given the following statements. 1. All popular textbooks have high prices

ID: 3196031 • Letter: W

Question

We are given the following statements.

1. All popular textbooks have high prices

2. No popular textbook exists only in print

3. The EECS 1028 textbook is popular

4. The EECS 1028 textbook has both electronic and print versions

5. The EECS 3101 textbook has low price

Use only the predicates Popular(x), OnlyPrint(x), LowPrice(x), and assume the negation of a low price is a high price.

1. (3 points) The EECS 1018 book has a high price

2. (3 points) The EECS 3101 book is popular Use only the predicates Popular(x), OnlyPrint(x), LowPrice(x).

The question asks you to check if each of the two conclusions are valid, given the facts numbered 1 through 5 preceding these statements.

Hints: Use the set of all textbooks as domain. Then

Popular(x): "x is popular"
OnlyPrint(x): "x exists only in print",

LowPrice(x): "x has a low price"

From the facts numbered 1 to 5 we can say that

Popular(x) --> ~LowPrice(x) and

LowPrice(x) --> OnlyPrint(x) --> ~Popular(x)

So from fact 3 EECS 1028 is popular so

Popular (EECS 1028) --> ~LowPrice( EECS 1028) implies EECS 1028 has a high price. So statement 1 is valid.

From fact 5 EECS 3101 has low price so

LowPrice (EECS 3101) --> OnlyPrint(EECS 3101) --> ~Popular(EECS 3101)

implies EECS 3101 is not popular. So statement 2 is not valid.

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