Translate these statements into English, where C ( x ) is “ x is a comedian” and F ( x ) is “ x is funny” and the domain consists of all people. a) ∀ x ( C ( x ) → F ( x ) ) b) ∀ x ( C ( x ) ∧ F ( x ) ) c) ∃ x ( C ( x ) → F ( x ) ) d) ∃ x ( C ( x ) ∧ F ( x ) )
Translate these statements into English, where C ( x ) is “ x is a comedian” and F ( x ) is “ x is funny” and the domain consists of all people. a) ∀ x ( C ( x ) → F ( x ) ) b) ∀ x ( C ( x ) ∧ F ( x ) ) c) ∃ x ( C ( x ) → F ( x ) ) d) ∃ x ( C ( x ) ∧ F ( x ) )
Let C(x) be the predicate " is a comedian", and let F(x) be the predicate" is
funny."
Match the statements below on the left to their equivalent English translations on
the right.
DOD
Vx(F(x) ^ C(x))
Vx (F(x) → C(x))
3x(F(x) V-C(x))
Vx-(F(x) ^ C'(x))
3x (F(x)^-C(x))
Vx (C(x)→-F(x))
1. All funny people are comedians.
Not all funny people are
comedians.
2.
3. No comedian is funny.
4. Everyone is a funny comedian.
It is not the case that everyone is a
funny comedian.
6. No one is a funny comedian.
5.
Let S(x) = “x is a student at Hostos Community College”; F(x) = “x is a faculty member at Hostos Community College”, and P(x,y) “x watched y at Regal Theaters” where the universe of discourse for x is all the people who are associated with Hostos Community College, and the universe for discourse for y is all movies.
Translate into Symbols: Some Hostos CC faculty member has not watched any movie at Regal Theaters.
If f(x) =
In x, g(x) = e X, and h(x) = x, find the following.
(a) (f o g)(x). What is the domain of fo g?
(b) (g o f)(x). What is the domain of go f?
(c) (fo g)(7)
(d) (f o h)(x). What is the domain of fo h?
(e) (fo h)( e)
Chapter 1 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
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