Set One Pair
by admin on Wednesday, February 24th, 2010 | No Comments
Set One Pair
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We say that two integers are near one another provided their difference is 2 or smaller.?
Let R stand for this is-near-to relation. Answer the following.
(a) Write down R as a set of ordered pairs. The answer should look like this:
R={(x,y) I ...}.
(b) Prove or disprove: R is reflexive.
(c) Prove or disprove: R is irreflexive.
(d) Prove or disprove: R is symmetric.
(e) Prove or disprove: R is antisymmetric.
(f) Prove or disprove: R. is transitive.
a. R = {(0,-2) ; (0,-1) ; (0,0) ; (0,1) ; (0,2) ; (1,0) ; (1,-1) ; (1,0) ; (1,1) ; (1,2) ; (1,3) ...}
b. true.. aRa because the a - a = 0 < 2
c. false... because all (a,a) is in R
d. true .. |a - b| = |b - a|
e. false
f. false (0,1) & (1,3) are in R but (0,3) is not.
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