Respuesta :
The maximum number of functions that can be defined from the power set of A, P(A), to the power set of B, P(B) is 4096.
The Collection of well-defined objects or elements is known as a set. The objects in a set are called elements. The Set contains a finite number of elements. The Set is denoted by any capital letter like A, B etc. Elements of the set can be numbers, alphabets etc.
The elements of the set are listed inside the curly brackets { ..... }. There are various types of sets. The set of all subsets of the set X is called a Power set including the null set, empty set and the set itself. Cardinal number or cardinality denotes the number of elements in the set. Cardinality is denoted by n( X ) where X is a set. The number of subsets of the set is given by 2^n.
As per the question,
- Set A = { a, b, c }
- Set B = { x, y }
⇒ n ( A ) = 3 elements
Number of subsets of A = 2³
= 8 subsets
⇒ n ( B ) = 2 elements
Number of subsets of B = 2²
= 4 subsets
By using the product rule,
Total number of functions from P ( B ) to P ( A ) = 8 × 8 × 8 × 8
= 4096
Therefore, 4096 is the maximum number of functions that can be defined from the power set of A, P(A) to the power set of B.
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