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Suppose (4,3) is a poset and for any pairs (x, y) and (a, b) in AxA define (x, y) ≤ (a, b) if and only if x ≤a and y≤ b. In the following list, select all of the correct statements. □ If a and b are elements of A such that a ≤ b then (a, b) ≤ (b, b). □ If a and b are elements of A such that a ≤ b then (c, a) ≤ (c, b) for any element c of A. □ If a, b and c are elements of A such that a ≤ b c then (a, b) and (a, c) are incomparable. There is a pair of incomparable elements in (AXA,≤) only if there is at least one pair of incomparable elements in (4,≤). None of these.

Suppose (4,3) is a poset and for any pairs (x, y) and (a, b) in AxA define (x, y) ≤ (a, b) if and only if x ≤a and y≤ b. In the following list, select all of the correct statements. □ If a and b are elements of A such that a ≤ b then (a, b) ≤ (b, b). □ If a and b are elements of A such that a ≤ b then (c, a) ≤ (c, b) for any element c of A. □ If a, b and c are elements of A such that a ≤ b c then (a, b) and (a, c) are incomparable. There is a pair of incomparable elements in (AXA,≤) only if there is at least one pair of incomparable elements in (4,≤). None of these.

Advanced Engineering Mathematics
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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Suppose (4,3) is a poset and for any pairs (x, y) and (a, b) in AxA define (x, y) ≤ (a, b) if and only if x ≤a and y≤ b. In the following list, select all of the correct statements. □ If a and b are elements of A such that a ≤ b then (a, b) ≤ (b, b). □ If a and b are elements of A such that a ≤ b then (c, a) ≤ (c, b) for any element c of A. □ If a, b and c are elements of A such that a ≤ b c then (a, b) and (a, c) are incomparable. There is a pair of incomparable elements in (AXA,≤) only if there is at least one pair of incomparable elements in (4,≤). None of these.
Transcribed Image Text:Suppose (4,3) is a poset and for any pairs (x, y) and (a, b) in AxA define (x, y) ≤ (a, b) if and only if x ≤a and y≤ b. In the following list, select all of the correct statements. □ If a and b are elements of A such that a ≤ b then (a, b) ≤ (b, b). □ If a and b are elements of A such that a ≤ b then (c, a) ≤ (c, b) for any element c of A. □ If a, b and c are elements of A such that a ≤ b c then (a, b) and (a, c) are incomparable. There is a pair of incomparable elements in (AXA,≤) only if there is at least one pair of incomparable elements in (4,≤). None of these.
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