Let the 6-tuple <B,+,*, c,0,1> be a Boolean algebra where B is a set, + and * the sum and the product operators respectively, 0 and 1 the zero and the unit elements respectively and c the complement operator.
If b is an element of the set B, what is the dual of the Boolean expression b + 1 = 1?
a) b * 1 = 1.
b) b * 1 = 1.
c) b + 0 = 0.
d) b * 0 = 0.
e) b * A = A.
change the operator. If b+1 = b, then b is the + identity (0)
So, change the operator and the identity element:
1*b = b
please answer
A
C
To find the dual of the Boolean expression b + 1 = 1, we need to interchange the operators + and * and replace 0 with 1 and 1 with 0.
The original expression b + 1 = 1 can be rewritten as:
b * c(1) = c(1)
The complement of 1 is 0, so we can replace c(1) with 0:
b * 0 = 0
Now, we can identify the dual expression by replacing * with + and 0 with 1:
b + 1 = 1
Therefore, the dual of the Boolean expression b + 1 = 1 is:
b * 0 = 0
Comparing the options given:
a) b * 1 = 1 - This is not the dual. We replaced + with * and 0 with 1, not 1 with 0.
b) b * 1 = 1 - This is the same as option a, and therefore, it is not correct.
c) b + 0 = 0 - This is incorrect as it is not the dual expression.
d) b * 0 = 0 - This matches the dual expression we derived.
e) b * A = A - This is not related to the dual expression.
So, the correct answer is:
d) b * 0 = 0