Final answer:
The compact notation for the boolean expression f(a,b,c) = a'b'c + ab'c + ab'c is intended to represent the minterms where the function evaluates to '1', which would be (1,5). However, none of the provided options correctly match this compact notation.
Step-by-step explanation:
The student's question pertains to finding a compact notation for a given boolean expression. The expression provided by the student is f(a,b,c) = a'b'c + ab'c + ab'c. To find the compact notation which usually corresponds to the minterms represented in the expression, we need to determine the minterm indices for which the function evaluates to '1'.
Here, the minterms are as follows:
- a'b'c represents the minterm where a=0, b=0, and c=1, which is minterm 1 (0,0,1 in binary is 1 in decimal)
- ab'c represents the minterm where a=1, b=0, and c=1, which is minterm 5 (1,0,1 in binary is 5 in decimal)
However, we notice there's a duplication in the expression, as ab'c is written twice, but this does not affect the compact notation as the minterm is only considered once.
So, the compact notation for the function is (1,5), since these are the minterm indices that result in the function evaluating to '1'. The correct answer from the options would be c. f(a,b,c) = (1,4,5), however, this contains a mistake because the index '4' should not be there, and the answer should actually be 'none of the above'.