Questions about logic.
Please Solve them ALL! (I have the right to ask the last question.)
Please write in a legible and annotated way, thank you.
Q1A)
Let P(x) be the statement “x can swim” and let Q(x) be the
statement “x can play the guitar.” Express each of these sentences
in terms of P(x), Q(x), quantifiers, and logical connectives. The
domain for quantifiers consists of all students in your
school.
a) No student in your school can swim or can play the guitar.
b) Every student in your school either can swim or can play the
guitar.
c) There is a student in your school who can swim and who play the
guitar.
d) There is a student in your school who can swim but who cannot
play the guitar.
Q1B)
Translate in two ways each of these statements into logical
expressions using predicates, quantifiers, and logical connectives.
First, let the domain consist of the students in your class and
second, let it consist of all people.
a) Everyone in your class has a computer.
b) Somebody in your class has seen a foreign movie.
c) There is a person in your class who cannot play the
guitar.
d) All students in your class can program.
e) Nobody in your class wants to have the flu.
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A recent alumnus of your university gifted two million dollars to the school to fund annual scholarships for needy students. The school expects to earn an average rate of return of 5.0 percent on the gift and to use all annual earnings for scholarships. What is the annual amount available for distribution as scholarships?
Group of answer choices
$40,000,000
$100,000
$20,000,000
$10,000,000
$50,000
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