very small doubt from ncert
its from misc exercis last question
Q number of binary operations on set {a,b} is??????
62priyam I think you are right.
I dont know where this question came from but answer has to be 23
1to define a binary operation , we have to define the values the operation takes for all values (x,y) where x,y belongs to S(it is a set)
this means that n*n operations have to be defined.
Each of the operations can take n values.
So total no. of operations = n^n^2
Therefore answer would be 16 operations.
33:D
well i got it...
i was wrong...
:P
It is asked no of operations..
so
a*b=a/b
a*a=a/b
b*a=a/b
b*b=a/b
Now no of binary operations = no of ways of selecting one from each line...
=2*2*2*2=16
[3]
Let one biary operation be #
so a#b=a
a#a=a
b#a=a
b#b=b
If any one line's result is changed then it would be other binary operation..
like wise other 15 combinations...
Sorry for confusing u all.. [3]
62haha..
no celestine, trust me i take u as among one of the most serious aspirants here..
I know that you have disagreed to ame a couple of times... but that is one reason I like you..
specially in 0.999999999999 and the paradox of probability ;)
9wat i gave is a well established formula from rd sharma
so u can trust me on this
i know its hard for nishant sir to trust me after my dubious reputation of posting wrong ans [3]
9fallacy in thoughts of priyam and nish :
u r neglecting relative premutation of the combos
62even if it is associative!
i think priyam has listed them correctly too!
AxA->A
9the binary table for set of n has n2 elements
now each box in that table is filled in n ways so
tot bin op = nn2 wen n is 2 its 16
9no priyam is wrong :( its 16 i had an exp for that but forgot now
thinking........
1binary operation tho set {1,2}x{1,2} me hotha hai..........
isme 2*2=4 elements hai
in binary operation 2 operands at a time
therefore no. of binary operation= 22*2=16
33a*a=a
a*a=b
a*b=a
a*b=b
b*b=a
b*b=b
b*a=a
b*a=b
i am not getting any more than these...
33are mere ko 8 lag raha hai...
Set A {a,b}
binary fn from AxA->A
_ * _ =_
three places two choice for each...
so 2*2*2=8.. ??[7][7]
24@ mani binary functions 4 kaise hote hain?????????
hum koi bhi binary function define kar sakte hain.......................compositon ,modulus,log,exponent.........etc. etc......
1hey vivek here
n=number of Elements inside the set
here set={a,b}
so we have 2 integers..............
so No of Binary Operations Possible== 222
==16
Got it Vivek!!!!!
