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.
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 36SE: The number of 5-element subsets from a set containing n elements is equal to the number of 6-element...
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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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