EXERCISE 1.9.2: Truth values for statements with nested quantifiers - small finite domain. The tables below show the values of predicates P(x, y), Q(x, y), and S(x, y) for every possible combination of values of the variables x and y. The row number indicates the value for x and the column number indicates the value for y. The domain for x and y is {1, 2, 3). P 1 23 1 T FT 2 T FT 3 T T F Q1 23 1 F FF 2 T TT 3 T F LL F S1 2 3 1 FF F 11 LL 2 F F F 3 F F F Indicate whether each of the quantified statements is true or false. (a) x P(x, y) (b) Q(x, y) (c) 3 x P(x, y) (d) 3x ³y S(x, y) (e) x ³ Q(x, y) (f) ³ P(x, y) (g) x P(x, y) (h) x ³у Q(x, y) (1)-(x,y) Feedback?
EXERCISE 1.9.2: Truth values for statements with nested quantifiers - small finite domain. The tables below show the values of predicates P(x, y), Q(x, y), and S(x, y) for every possible combination of values of the variables x and y. The row number indicates the value for x and the column number indicates the value for y. The domain for x and y is {1, 2, 3). P 1 23 1 T FT 2 T FT 3 T T F Q1 23 1 F FF 2 T TT 3 T F LL F S1 2 3 1 FF F 11 LL 2 F F F 3 F F F Indicate whether each of the quantified statements is true or false. (a) x P(x, y) (b) Q(x, y) (c) 3 x P(x, y) (d) 3x ³y S(x, y) (e) x ³ Q(x, y) (f) ³ P(x, y) (g) x P(x, y) (h) x ³у Q(x, y) (1)-(x,y) Feedback?
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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Transcribed Image Text:EXERCISE 1.9.2: Truth values for statements with nested quantifiers - small finite domain.
The tables below show the values of predicates P(x, y), Q(x, y), and S(x, y) for every possible combination of values of the variables x
and y. The row number indicates the value for x and the column number indicates the value for y. The domain for x and y is {1, 2, 3).
P 1 2 3
1 T
2 T
H
3
F T
TI
FT
Q 1 2 3
1 F F F
2 T
TT
S1 2 3
1 F
LL
T TF 3 T FF 3
TIN
LL
F
F
2 F F F
1
LL
F
F
LL
Indicate whether each of the quantified statements is true or false.
(a) 3x vy P(x, y)
(b) 3x by Q(x, y)
(c) Эy vx P(x,y)
(d) 3x ³y S(x, y)
(e) vx ³y Q(x, y)
(f) x ³ P(x, y)
(g) vxv P(x, y)
(h) 3x ³y Q(x, y)
(1)-(x, y)
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