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if a*c = c*a and b*c = c*b, then (a*b)*c = c*(a*b)

Discrete structure

Prob. Let (A, ) be a semigroup. Show that for a, b, c ∈ A, if ac = ca and bc = cb, then (ab)c = c(a*b).

Solution:

Discrete Structure

  • SET
  • Mathematical induction
  • Relation
  • Binary operations
  • Show that- (P∩Q)X(R∩S) = (PXR)∩(QXS)
  • prove that – (A∩B)X(C∩D) = (AXC)∩(BXD)
  • Prove that- A∩(B∪C) = (A∩B) ∪ (A∩C)
  • prove that- AX(B∩C) = (AXB) ∩ (AXC)
  • Binary operations
  • Group
  • Algebraic structure
  • Show that (…, -4, -3, -2, -1, 0, 1, 2, 3, 4,…} is group
  • Show that a*b=b*a
  • if a*c = c*a and b*c = c*b, then (a*b)*c = c*(a*b)

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