(d) Prove or disprove that, for any universal set U and predicate P VxU, P(x)][3x € U, P(x)]
(d) Prove or disprove that, for any universal set U and predicate P VxU, P(x)][3x € U, P(x)]
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 18E: In Exercises , prove the statements concerning the relation on the set of all integers.
18. If ...
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![(b)
nd Q
UP()) (x = U, Q(x))] = U.P(z) AQ(@)]
Prove or disprove that, for any
(d)
Prove or disprove that, for any universal set U and predicate P
VxU, P(x)] [3x € U, P(x)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a5f7442-d906-42f0-83ac-3af4f7174a28%2F573c258c-4274-41d3-ba0d-69ea21359be9%2Fqhqss7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b)
nd Q
UP()) (x = U, Q(x))] = U.P(z) AQ(@)]
Prove or disprove that, for any
(d)
Prove or disprove that, for any universal set U and predicate P
VxU, P(x)] [3x € U, P(x)]
![(6)
[(JXEU, P(X) ^ (FXEU, Q(x))] → [FREU, PEDAQ(x)]
Λ
This
statement
is
false
Let
U= {1, 12}
'
P(x) x < 4
and
Q(x):×79
true
So
3x EU, P(x)
[As P(i): 4,50
i U
I is
such
x]
and
Jx EU, Q(x)
is
also
true [12 is
Such
x m U]
But
#XEU, P(x) A Q(x)
statement
false
So
the
given
(© [3xEU, P(x)] = [+x=U, P(x)]
(c)
This
statement
false
Let
U = {1123
P(x) :
×<5
So
that
P(1):
145
is
true
So
ξχευ, (α)
Now
P(12): 1245
is false
So
* XEU, P(x)
is false
statement
is
So
the
given
false.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a5f7442-d906-42f0-83ac-3af4f7174a28%2F573c258c-4274-41d3-ba0d-69ea21359be9%2F0cwp9eg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(6)
[(JXEU, P(X) ^ (FXEU, Q(x))] → [FREU, PEDAQ(x)]
Λ
This
statement
is
false
Let
U= {1, 12}
'
P(x) x < 4
and
Q(x):×79
true
So
3x EU, P(x)
[As P(i): 4,50
i U
I is
such
x]
and
Jx EU, Q(x)
is
also
true [12 is
Such
x m U]
But
#XEU, P(x) A Q(x)
statement
false
So
the
given
(© [3xEU, P(x)] = [+x=U, P(x)]
(c)
This
statement
false
Let
U = {1123
P(x) :
×<5
So
that
P(1):
145
is
true
So
ξχευ, (α)
Now
P(12): 1245
is false
So
* XEU, P(x)
is false
statement
is
So
the
given
false.
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