14. Let A be a nonempty set, and let P(A) be partially ordered by set inclusion. Dio Isin Show that A1s2 od nol robro isinsq 8 od A 1 (a) if Be P(A) and x e B, then B-{x} is an immediate predecessor of B. T) (b) if B E P(A) and x B, then B is an immediate predecessor of B U {x}. no obio Ieiticg s2TIadi ov011 ( bas A lo rsb1o
14. Let A be a nonempty set, and let P(A) be partially ordered by set inclusion. Dio Isin Show that A1s2 od nol robro isinsq 8 od A 1 (a) if Be P(A) and x e B, then B-{x} is an immediate predecessor of B. T) (b) if B E P(A) and x B, then B is an immediate predecessor of B U {x}. no obio Ieiticg s2TIadi ov011 ( bas A lo rsb1o
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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please help me on question 14
Transcribed Image Text:(D)
13. For the partially ordered set A = (u
below, find
* (a) all upper bounds for the sets {g,h}, {e,h}, {a, h}, {C,f,g}, and {b.f..
(b) all lower bounds for the sets {g, h}, {f, h}, {b, c, d}, {c,f, g}, and s"}.
(c) the supremum, if it exists, for the sets {8, n}, 18, C}, 1e, 8, h}, {b f".
vad no
obro leine
Isinsq bne b d) the infimum, if it exists, for the sets {b, e,f }, {e, 8}, {b,c, d}, and {be
ng ginitab e
(e) the smallest element, if it exists, for the sets {b, c, f }, {e, g}, {b .
and {b, f, g}.
20
d.
a
9.
=D T0 d A li vino bas tA
e Tol ow Todto
f
Isirisq
(d)
Do ow
e
(d+n bng d ADylno bns lid o
Isitusq s
1BTIsg B 014. Let A be a nonempty set, and let P(A) be partially ordered by set inclusion.
i rot nobio Isin Show thatE A192 od ol robio isinsg s od X 1o
a lle 101 awll (a) if Be P(A) and x e B, then B- {x} is an immediate predecessor of B.
bolleo ai T).2 (b) if Be P(A) and x 4 B, then B is an immediate predecessor of B U {x}.
8x A no 19bno Isiticg si T adi ovo11 (2 bas S
bas A lo sbio
* (a) all for the sets {e, g,h}.
* (b) all for the sets {g, h}, {f, h}, {b, c, d}, {c,f, g}, and {a,d}.
(c) the if it for the sets {g, h}, {g, c}, g, h}, g},
osved no 13. For the set A=
(e) the if it for the {b, c, f}, {e, {b, c, d},
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