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  3. 5 r is the relation on the integers given by...

Question: 5 r is the relation on the integers given by...

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5) R is the relation on the integers given by R(n, m): n+ m ends with 0. For example, R(18, 102) is true since 18102 120, and 120 does end with a 0. But 55+ 11 66 so R(55,11) is false since 66 does not end with a 0. Circle all the properties the relation R has in the list below (a) Reflexive (b) Symmetric (c) Antisymmetric (d) Transitive (e) R has none of those four properties. 6) Let R be the relation from 1,2,3,4} to r, y given by R {(1, x), (1,y), (2, r), (3, y), (4,r)) and iet S be the relation from {r, y} to {a,b, c} given by S-((x, a), (z,c), (y,b)) Circle all the ordered pairs that are in S o R 7) Let A1,2,3,4 and let B 2,4,6,8. Circle all the true statements in the list below (b) (2,2) E Ax B (c) 2 EA-B (d) 2 E AUB (e) (2,2) e Bx A 8) Let C be the relation on the cards in the usual 52 card deck defined by C(z,y): z and y have the same suit. Circle all the true statements in the list below (a) The equivalence class, [34], of the 34 contains exactly 13 elements. (b) The equivalence class, 34], of the 34 contains exactly 4 elements. (c) 34-4 (d) [3 -1341 (e) None of the above statements are true

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