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Let X = {a,b,c,d} and let be the binary operation on X given by the following table:
a b c d
a d c a b
b c b a c
c a a d c
d b d c a
(e) Is the subset Y = {a, c, d} of X closed under ? Explain.
Solution
Let X = {a,b,c,d} and let be the binary operation on X given by the following table:
a b c d
a d c a b
b c b a c
c a a d c
d b d c a
(e) Is the subset Y = {a, c, d} of X closed under ? Explain.
if x, y Y then x y Y then it is closed as Y subset of X
as Y = {a,c,d}
x,y can only be a,c,d so
we check
a*c = a
c*a = a
a*d = b
d*a = b
c*d = c
d*c = c
as we can see there is extra element b so it is not closed

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Let X - {a-b-c-d} and let be the binary operation on X given by the f.docx

  • 1. Let X = {a,b,c,d} and let be the binary operation on X given by the following table: a b c d a d c a b b c b a c c a a d c d b d c a (e) Is the subset Y = {a, c, d} of X closed under ? Explain. Solution Let X = {a,b,c,d} and let be the binary operation on X given by the following table: a b c d a d c a b b c b a c c a a d c d b d c a (e) Is the subset Y = {a, c, d} of X closed under ? Explain. if x, y Y then x y Y then it is closed as Y subset of X as Y = {a,c,d} x,y can only be a,c,d so we check a*c = a c*a = a a*d = b d*a = b
  • 2. c*d = c d*c = c as we can see there is extra element b so it is not closed