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  • Tell me? Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A x B, eachhaving at least three elements is :

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A x B, each

having at least three elements is :

  • Option 1)

    219

  • Option 2)

    256

  • Option 3)

    275

  • Option 4)

    510

 

Answers (1)

best_answer

As we learnt in

SUBSETS -

A set A is said to be a subset of a set B if every element of A is also an element of B.

- wherein

It is represented by \subset. eg. A \subset B if A={2,4} and B= {1,2,3,4,5}

 

 

 

 Let Ahaving elements {a, b, c, c} and B having {e, f}

Then A\times B having 8 elements and no. of subsets = 28 = 256

Now, No. of subsets = \phi (ae), ......(df) and (ae, be)........... 7 elements.

Similarly  7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 (having two elements)

and g having sinle element including \phi

\therefore    28 + 9 = 37

\therefore    Atleast three elements = 256 - 37 = 219 

Correct option is 1.


Option 1)

219

This is the correct option.

Option 2)

256

This is an incorrect option.

Option 3)

275

This is an incorrect option.

Option 4)

510

This is an incorrect option.

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