Section 1.4 Nested Quantifiers 1.4.1
1.4 NESTED QUANTIFIERS
Example 1.4.1: Every sophomore owns a
computer or has a friend in the junior class who
owns a computer.
Domains Sand Jare the sophomores and the
juniors. Predicates C(u) and F(v, w) mean that
uowns a computer and that wis a friend of v.
(∀x∈S)C(x)∨(∃y∈J)[F(x, y)∧C(y)].
disambiguation: Specify the domain when not
evident from context. Use brackets to identify
scope of quantifiers.
TRANSPOSING QUANTIFIERS
Be careful about transposing different kinds of
quantifiers.
(∀x)(∃y)[x2≤y] is true.
(∃y)(∀x)[x2≤y] is false.
However, you can safely transpose two quantifiers
of the same kind.
Coursenotes by Prof. Jonathan L. Gross for use with Rosen: Discrete Math and Its Applic., 5th Ed.
