The sum of all the minterms of a boolean function of 2 variables is equal to 1.
Answers
The sum of all the minterms of a boolean function of n variables is equal to 1.
Prove the above statement for n=3.
a'b'c' + a'b'c + a'bc' + a'bc + ab'c' + ab'c + abc' + abc = a'b' + a'b + ab' + ab = a' + a = 1.
Answer:A Boolean function is a mathematical function that takes in one or more Boolean variables (i.e., variables that can take on the values 0 or 1) and returns a Boolean value. In the case of a Boolean function of 2 variables, there are 4 possible combinations of input values (0 or 1) for the two variables.
Explanation:
In the case of a Boolean function of 2 variables, there are 4 possible minterms (also known as canonical forms) that represent the different combinations of input values. These minterms are:
x1x2: the minterm that corresponds to the function output being 1 when both x1 and x2 are 1
x1'x2: the minterm that corresponds to the function output being 1 when x1 is 0 and x2 is 1
x1x2': the minterm that corresponds to the function output being 1 when x1 is 1 and x2 is 0
x1'x2': the minterm that corresponds to the function output being 1 when x1 is 0 and x2 is 0
The sum of all the minterms of a Boolean function of 2 variables is equal to 1, this is because each minterm corresponds to one of the four possible combinations of input values, and together, these four combinations cover all possible input values.
In other words, the sum of all the minterms of a Boolean function of 2 variables is equal to 1 because the Boolean function must evaluate to 1 for at least one of the four.
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