Let A: {1, 2, 3, 4, 5, 6, 7}. Define B = {T 
A : either 1 
T or 2 
T } and C = T 
A : T the sum of all the elements of T is a prime number}. Then the number of elements in the set B 
C is_______________
Text Solution
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(107)
is a set containing sub sets of 
containing element 1 and not containing 2 .
And 
is a set containing subsets of 
whose sum of elements is not prime.
So, we need to calculate number of subsets of 
whose sum of elements plus 1 is composite.
Number of such 5 elements subset 
Number of such 4 elements subset 
(except selecting 3 or 7 )
Number of such 3 elements subset 
(except selecting 
or 
)
Number of such 2 elements subset 
(except selecting 
)
Number of such 1 elements subset 
(except selecting 
or 
)
Number of such 0 elements subset 
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