Define ∗ on Z by x ∗ y = x + y + 4. Then: (a) Prove that ∗ is a binary operation on Z.  (b) Show that ∗ is an associative operation on Z.  (c) Determine the identity element for ∗ in Z.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Define ∗ on Z by x ∗ y = x + y + 4. Then:

(a) Prove that ∗ is a binary operation on Z. 
(b) Show that ∗ is an associative operation on Z. 
(c) Determine the identity element for ∗ in Z.

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