1. Write each of the statements using variables and quantifiers: a) Some integers are perfect squ...
1. Write each of the statements using variables and quantifiers:
a) Some integers are perfect squares.
b) Every rational number is a real number.
2. Let P(x) = "x has shoes", Q(x) = "x has a shirt", and R(x,y) = "x is served by y". The universe of x is people. Rewrite the following predicates in words:
a) ∀x∃y [(¬P(x) ∧ Q(x)) ⇒ ¬R(x,y)]
b) ∃x∃y [(¬P(x) ∧ Q(x)) ∧ R(x,y)]
c) P("Bill" ) ∨ (Q("Jim") ∧ ¬Q("Bill")) ⇒ R("Bill","Jim")
Homework Answers
I(x) = x is an integer
P(x) = x is a perfect square
R(x) = x is a rational number
L(x) = x is a real number
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