Total no. of Binary operation

• Dec 25th 2011, 06:09 PM
nikhilbhr
Total no. of Binary operation
Given a set of elements {a,b,c,d} ,then find the total no. of binary operations that can be defined on x ?
• Dec 25th 2011, 09:51 PM
CaptainBlack
Re: Total no. of Binary operation
Quote:

Originally Posted by nikhilbhr
Given a set of elements {a,b,c,d} ,then find the total no. of binary operations that can be defined on x ?

This is asking for the number of mappings from D={a,b,c,d}x{a,b,c,d} into R={a,b,c,d}.

Well there are 16 elements in D, and each can be mapped to any of the 4 elements of R.

CB
• Dec 26th 2011, 12:29 AM
nikhilbhr
Re: Total no. of Binary operation
In this way answer to this question is 4^16 ..But in the book answer to this question was 2^16 ...Please tell me which one is right..
Thanx for help
• Dec 26th 2011, 03:54 AM
Plato
Re: Total no. of Binary operation
Quote:

Originally Posted by nikhilbhr
In this way answer to this question is 4^16 ..But in the book answer to this question was 2^16 ...Please tell me which one is right.

That is almost certainly a typo in the solution manual.