Solution.
A.
{x∣x is real numbers and x2=1}={−1,1}.
{x∣x is an integer and −4<x≤3}={−3,−2,−1,0,1,2,3}.
B.
{a,e,i,o,u}={x∣x is vowels letters, without ’y’ }.
{−2,−1,0,1,2}={x∈Z∣∣x∣=2}.
C.
A=(a,b,c),B=(x,y),C=(0,1).
AUC={a,b,c,0,1}.C×B={(0,x),(0,y),(1,x),(1,y)}.B−A={x,y}.(A∩C)UB={x,y}.
D.
An=2⋅3n+5.A0=7.A5=491.A3=59.A8=13127.A2=23.∑An=∞.
E.
X={−1,0,1,2,3,4,5}.R={(x,y)∣x≤y}.
F.
R={(−1,0),(−1,1),(−1,2),(−1,3),(−1,4),(−1,5),(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(5,5),(4,4),(3,3),(2,2),(1,1),(0,0),(−1,−1)}.
G.
Domain(R )={−1,0,1,2,3,4,5}.
H.
Range(R )={−1,0,1,2,3,4,5}.
I.
J.
Properties of the Relation:
Reflexivity
Irreflexivity
Symmetry
Antysymmetry
Asymmetry
Transitivity.
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