(f.) Let X and Y be finite sets. If there exists a function f : X → Y that is one-to-one, then |X|≤|Y| (g.) If a set S is countable, then its powerset P(S) is also countable. (h.) The infinite union of finite sets is countable. (i.) Let F(x)= x². F is an automorphism on (R+,.) (j.) The set of non-zero real numbers with arithmetic multiplication as an operation is a
(f.) Let X and Y be finite sets. If there exists a function f : X → Y that is one-to-one, then |X|≤|Y| (g.) If a set S is countable, then its powerset P(S) is also countable. (h.) The infinite union of finite sets is countable. (i.) Let F(x)= x². F is an automorphism on (R+,.) (j.) The set of non-zero real numbers with arithmetic multiplication as an operation is a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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answer f to j only
Transcribed Image Text:Choose O if the statement is ALWAYS true.
Otherwise, choose X. No need for justifications.
◆ (a.) The logic expressions
(p → (q→r)) and ((p ^ q) →r) are logically
equivalent.
◆ (b.) Suppose the proposition p V q is true,
but we do not know which of p or q is true. If
p→r and q→ r, then regardless of which of p or
q is true, then we can infer proposition r to be true.
♦ (c.) Let A be a finite set of n elements.
Then the number of subsets of A is n².
(d.) If the symmetric difference of two
sets is empty, then those two sets are equal.
+ (e.) Consider the divides relation
x Ryxy. If R is defined over the set of all
integers Z, then R is a partial-order relation.
♦ (f.) Let X and Y be finite sets. If there exists a
function f : X→ Y that is one-to-one, then X ≤ Y
powerset P(S) is also countable.
◆
(g.) If a set S is countable, then its
(h.) The infinite union of finite sets is
countable.
→
(i.) Let F(x)=
automorphism on (R+, .)
-
x². F is an
♦ (j.) The set of non-zero real numbers with
arithmetic multiplication as an operation is a
monoid, but not a group.
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