On the set A={a,b,c,d} the table gives the operation 'o' and on the set B={1,2,3,4} th the operation *. Find out if there is an isomorphism between groupoids (A,o), (B,*). If there is the isomorphism, find it, otherwise justify its non-existence. * a bc d 1 2 3 4 a a a a 1|4 2 2 1 ba b c d 2 2 4 2 2 a c b a 3 2 2 4 3 d a d a b 4 1 2 3 4
On the set A={a,b,c,d} the table gives the operation 'o' and on the set B={1,2,3,4} th the operation *. Find out if there is an isomorphism between groupoids (A,o), (B,*). If there is the isomorphism, find it, otherwise justify its non-existence. * a bc d 1 2 3 4 a a a a 1|4 2 2 1 ba b c d 2 2 4 2 2 a c b a 3 2 2 4 3 d a d a b 4 1 2 3 4
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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Transcribed Image Text:On the set A={a,b,c,d} the table gives the operation 'o' and on the set B={1,2,3,4} the table gives
the operation *".
Find out if there is an isomorphism between groupoids (A,0), (B,*).
If there is the isomorphism, find it, otherwise justify its non-existence.
a
b
C
d
*
1 2 3 4
a
b
a
a
a
1|4 2 2 1
b
a
c d
2 | 2 4 2 2
a
c b
a
3 2 2 4 3
d
a
d
a b
4 |1 2 3 4
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