The total number of functions, f:{1,2,3,4}.(1,2,3,4,5,6} such that f(1) + f(2) = f(3), is equal to :
Text Solution
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A={1,2,3,4}
B = {1,2, 3, 4, 5, 6}
Here f(3) can be 2, 3,4, 5, 6
f(3) = 2, (f(1), f(2)) 
(1,1) 
6 cases
f(3) = 3,(f(1),f(2)) 
(1,2),(2,1)
2x6=12cases
f(3) - 4, (f(1), f(2)) 
(1,3), (3,1), (2,2)
3 x 6= 18 cases
f(3) = 5, (f(1), f(2)) 
(1,4), (4,1), (2,3), (3,2)
4 x 6 = 24 cases
f(3) = 6, (f(1), f(2)) 
(1,5),(5,1),(2,4),(4,2),(3,3)
5 x 6 = 30 cases
Total number of cases = 6+ 12 + 18 + 24 + 30 = 90
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