Question

Let S = {1, 2, 3, 4 }.

The total number of unordered pairs of disjoint subsets of S is equal to

(a) 25

(b) 34

(c) 41

(d) 42

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Answer 1

ANSWER:-------------

{ 4 elements so total no of such subsets is 3^4Now since this subsets are unordered }

i.e

{1,2}={2,1} we need to divide our earlier no by 2 and keep in mind that for { },{ } we have only 1 choice

{So our solution will be (3^4+1)/2=(81+1)/2=41}

{More generally for n elements we have}

(3^n-1)/2+130 

HOPE IT HELPS:--

THANKS!!!!!

Answer 2

Answer:

Option(c)

Step-by-step explanation:

Shortcut Method:

Total number of unordered pairs = (3⁴ + 1)/2

                                                       = (81 + 1)/2

                                                       = 82/2

                                                       = 41.

Hope it helps!