If A = {1,2,3,4,5), and if F:P(A) → Z is such that -- then determine the value of [0, if X has an even number of elements F(X)= 1, if X has an odd number of elements F({1,3,4}). (Here, P(A) is the power set of A) .
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Therefore the value of F(X) = 1
Given:
A = {1,2,3,4,5), and if F:P(A) → Z
F(X) = 0 if X has an even number of elements
F(X) = 1 if X has an odd number of elements
To find:
F(X)
Solution:
The function F is defined such that it assigns a value to each subset of A based on the number of elements in the subset. Specifically, if a subset X of A has an even number
The function F maps the power set of A (P(A)) to the set of integers (Z). It is defined such that if X has an even number of elements, F(X) = 0, and if X has an odd number of elements, F(X) = 1.
Given the set X = {1,3,4}, we can see that X has an odd number of elements (3 elements). Therefore, the value of F(X) = 1.
Therefore the value of F(X) = 1
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