Chapter 1: Q42E (page 68)
Use quantifiers to express the distributive laws of multiplication over addition for real numbers.
The quantifiers too express the distributive law of multiplication over addition for real numbers can be determined.
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Let and be the statements “xis a clear explanation,” “xis satisfactory,” and “xis an excuse,” respectively. Suppose that the domain for x consists of all English text. Express each of these statements using quantifiers, logical connectives, and and .
a) All clear explanations are satisfactory.
b) Some excuses are unsatisfactory.
c) Some excuses are not clear explanations.
d) Does (c) follow from (a) and (b)?
Suppose that Prolog facts are used to define the predicates motherand fatherwhich represent that Mis the mother of Yand Fis the father of X, respectively. Give a Prolog rule to define the predicate grandfather ,which represents that Xis the grandfather of Y. [Hint: You can write a disjunction in Prolog either by using a semicolon to separate predicates or by putting these predicates on separate lines.]
Determine whether these biconditionals are true or false.
a)if and only if
b)if and only if
c)if and only if monkeys can fly.
d) if and only if
Freedonia has fifty senators. Each senator is either honest or corrupt. Suppose you know that at least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt. Based on these facts, can you determine how many Freedonian senators are honest and how many are corrupt? If so, what is the answer?
You are eligible to be President of the U.S.A. only if you are at least 35 years old, were born in the U.S.A, or at the time of your birth both of your parents were citizens, and you have lived at least 14 years in the country. Express your answer in terms of e: “You are eligible to be President of the U.S.A.,” a: “You are at least 35 years old,” b: “You were born in the U.S.A,” p: “At the time of your birth, both of your parents where citizens,” and r: “You have lived at least 14 years in the U.S.A.”
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