1. Let H(x) be the statement “x is happy," where the domain is the set of dogs. A. How would you write the statement "all dogs are happy" in the symbols of predicate logic? B. The negation of a statement is its logical opposite; it is true when the statement is false, and false when the statement is true. Write the negation of the statement "all dogs are happy" in English, and also in symbols.

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1. Let H(x) be the statement “x is happy," where the
domain is the set of dogs.
A. How would you write the statement "all dogs
are happy" in the symbols of predicate logic?
B. The negation of a statement is its logical
opposite; it is true when the statement is false,
and false when the statement is true. Write
the negation of the statement "all dogs are
happy" in English, and also in symbols.
2. Let X be the set of real numbers in the interval 0 <
x < 1. Consider the following statement: For every
number x in X, there is a number y in X such that
y < x.
A. Decide whether this statement is true or false.
B. Write the negation of this statement in
English.
C. Write the above statement, and its negation, in
the symbols of predicate logic.
3. Based on your work above, state some symbolic
rules you can use to negate a quantified
statement.
Transcribed Image Text:1. Let H(x) be the statement “x is happy," where the domain is the set of dogs. A. How would you write the statement "all dogs are happy" in the symbols of predicate logic? B. The negation of a statement is its logical opposite; it is true when the statement is false, and false when the statement is true. Write the negation of the statement "all dogs are happy" in English, and also in symbols. 2. Let X be the set of real numbers in the interval 0 < x < 1. Consider the following statement: For every number x in X, there is a number y in X such that y < x. A. Decide whether this statement is true or false. B. Write the negation of this statement in English. C. Write the above statement, and its negation, in the symbols of predicate logic. 3. Based on your work above, state some symbolic rules you can use to negate a quantified statement.
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