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In the following list, select all the correct statements, if (4,) is a poset and for any elements (x,y) and (a,b) in AxA: (x,y) ≤ (a,b) if and only if x ≤a and y 3b. □ (AXA,) is a poset. □ If (4,3) is a total order then (AXA,) is also a total order. If there exist a and b in A such that a ≤ b in (4,≤), then (a,b) ≤ (b,b) in (AXA,≤). If there exist a and b in A such that a ≤ b in (4,≤), then (a,c) ≤ (b,c) in (AXA,<) for every element c of A. O None of these.

In the following list, select all the correct statements, if (4,) is a poset and for any elements (x,y) and (a,b) in AxA: (x,y) ≤ (a,b) if and only if x ≤a and y 3b. □ (AXA,) is a poset. □ If (4,3) is a total order then (AXA,) is also a total order. If there exist a and b in A such that a ≤ b in (4,≤), then (a,b) ≤ (b,b) in (AXA,≤). If there exist a and b in A such that a ≤ b in (4,≤), then (a,c) ≤ (b,c) in (AXA,<) for every element c of A. O 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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In the following list, select all the correct statements, if (4,) is a poset and for any elements (x,y) and (a,b) in AxA: (x,y) ≤ (a,b) if and only if x < a and y 3b. □ (AXA,<) is a poset. □ If (4,3) is a total order then (AXA,) is also a total order. □ If there exist a and b in A such that a ≤ b in (4,3), then (a,b) ≤ (b,b) in (AXA,≤). □ If there exist a and b in A such that a ≤ b in (4,≤), then (a,c) ≤ (b,c) in (AXA,≤) for every element c of A. O None of these.
Transcribed Image Text:In the following list, select all the correct statements, if (4,) is a poset and for any elements (x,y) and (a,b) in AxA: (x,y) ≤ (a,b) if and only if x < a and y 3b. □ (AXA,<) is a poset. □ If (4,3) is a total order then (AXA,) is also a total order. □ If there exist a and b in A such that a ≤ b in (4,3), then (a,b) ≤ (b,b) in (AXA,≤). □ If there exist a and b in A such that a ≤ b in (4,≤), then (a,c) ≤ (b,c) in (AXA,≤) for every element c of A. O None of these.
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