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+22 votes

Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is

  1. $z^{2^{xy}}$
  2. $z \times 2^{xy}$
  3. $z^{2^{x+y}}$
  4. $2^{xyz}$
asked in Set Theory & Algebra by Loyal (4.3k points)
edited by | 786 views

4 Answers

+25 votes
Best answer

D is Correct.

E = 2XY  Which is the total number of subsets of W.

Now, the mapping for a function from A to B with N and M elements respectively... we have $M^{N}$ .


EZ = 2XY(Z) = 2XYZ

answered by (393 points)
edited by
+8 votes
çardinality of set W = x*y

and E is set of all subsets of W which means E is power set of W so cardinality of set E = 2^(x*y)

now we have cardinalities of both E and Z so number of functions from Z to E will be (cardinality of E)^(cardinality of Z) so ans is 2^(x*y*z)
answered by (119 points)
+3 votes

W = X  ⨉ Y   ,∣ W ∣ = xy

E = powerset of ( X  ⨉ Y  ) , ∣ E ∣ = 2xy

Let f be the function , f : Z ---> E 

Total number of functions from Z ---> E  =  ∣ E ∣ ∣ Z ∣ = 2xyz

The correct answer is ,(D) 2xyz

answered by Veteran (16.3k points)
0 votes
ans (D)
answered by Boss (5.2k points)
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