1. Consider the relation c on A (1,2,3) consisting of 1 c 2.2 c 3 and 2 C 2 (and
ID: 3013478 • Letter: 1
Question
1. Consider the relation c on A (1,2,3) consisting of 1 c 2.2 c 3 and 2 C 2 (and nothin lse). Which laws does this relation satisfy? Circle all that apply: Irreflexivity Transitivity Comparability 2. Consider the relation c on A N where acb ie a divides which laws does this relation satisfy? Circle all that apply: Irreflexivity Transitivity Comparability 3. Consider the relation Con A iff a which laws does this relation satisfy? N where acb b. Circle all that apply: Irreflexivity Transitivity Comparability 4. Consider the set A (1,2 u 13) u (4,5]? Do any elements of A have an immediate successor? Circle YES or No. 5. Do the sets (1,6) and (-5, 10) under their usual inherited orderings have the same order type? Circle YES or NO. 6. Do the sets (-1,1) and (3,6) under their usual orderings have the same order type? Circle YES or NO. 7. Set Bi (-1,i 1) for all i e N Does Bi have a supremum? Circle YES or No. 8. Set Bi [-1, 1/i) for all i e N Does nieNBi have a supremum? Circle YES or NO.Explanation / Answer
1) yes irreflexivity since x not related x for any x
1 C 2 , 2C 3 but 1 is not related to 3
hence relation is not transitive
not transitivity
comparability is also not statisfied since neithet 1 is related to 3 nor vice versa
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