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Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.
Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?
Correct answer is '4'. Can you explain this answer?
Most Upvoted Answer
Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of...
The main part of the question is to understand that each 1 in the binary sequence represents an element of the set. If the nth bit is 1, n is there in the set, else not.
Hence, we have A = {1, 2, 3, 4, 5, 9} B = {1,2, 3, 4, 7, 8} 
c = { 1,4, 5, 6, 9} Now, D is set of those elements which appear in exactly two of A, B and C.
Hence, D = {2, 3, 5, 9} Hence, D can be represented by 100010110.
Sum = 4
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Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer?
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