Question 34 Prove: If is an associative operation on S, then a* * * (b* (cd)) = a* ((b*c) * d) = (a + b) * (cd) = (a* (b*c)) *d = ((a + b) *c) * d for all a, b, c, d Є S. Question 35 Assume that * is an operation on S with identity element e, and that I* *(y * z) = (x*2) * y for all x, y, z S. Prove that is commutative and associative. Question 36 Assume that e is an identity element for an operation * on a set S. If a, b Є S and a*b=e, then a is said to be a left inverse of b and b is said to be a right inverse of a. Prove that if ✶ is associative, b is a left inverse of a, and c is a right inverse of a, then b=c.
Question 34 Prove: If is an associative operation on S, then a* * * (b* (cd)) = a* ((b*c) * d) = (a + b) * (cd) = (a* (b*c)) *d = ((a + b) *c) * d for all a, b, c, d Є S. Question 35 Assume that * is an operation on S with identity element e, and that I* *(y * z) = (x*2) * y for all x, y, z S. Prove that is commutative and associative. Question 36 Assume that e is an identity element for an operation * on a set S. If a, b Є S and a*b=e, then a is said to be a left inverse of b and b is said to be a right inverse of a. Prove that if ✶ is associative, b is a left inverse of a, and c is a right inverse of a, then b=c.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with q36, 35 and 34
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Question 34 Prove: If is an associative operation on S, then
a * (b* (cd)) = a* ((b*c) * d) = (a + b) * (cd) = (a* (b*c)) *d = ((a + b) *c) * d
for all a, b, c, de S.
Question 35 Assume that is an operation on S with identity element e, and that
x*(y* z) = (x * 2) * y
for all x, y, z S. Prove that is commutative and associative.
Question 36 Assume that e is an identity element for an operation * on a set S. If a, b E S and
a+b=e, then a is said to be a left inverse of b and b is said to be a right inverse of a.
Prove that if ✶ is associative, b is a left inverse of a, and c is a right inverse of a, then
b = c.
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