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1.  A set S has 5 elements. How many ways we can choose subsets P and Q ,so that P intersection Q is null.?
2. A fruit salad can be made using at least one of the fruits mango, apple, pineapple, watermelon and banana. How many varieties os salad possible?

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Anonymous 1 Comment

first we can select a set for P and then for Q

6 cases will occur:

case 1: P is NULL set then Q can have 2^5 options.ways=2^5

case 2: p contains set with 1 element i.e. 5c1 and q will contain      2^4(we will remove the element given to p and count the no. of subsets formed with remaining 4 elements).ways=5*2^4

similarly

case 3: ways=5c2*2^3

case 4:ways=5c3*2^2

case 5: ways=5c4*2^1

case 6: ways=5c5*2^0(complete set and null set).

total ways=sum all the six cases.

plz correct if wrong.

could you copy this solution in to first.

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first we can select a set for P and then for Q

6 cases will occur:

case 1: P is NULL set then Q can have 2^5 options.ways=2^5

case 2: p contains set with 1 element i.e. 5c1 and q will contain 2^4(we will remove the element given to p and count the no. of subsets formed with remaining 4 elements).ways=5*2^4

similarly

case 3: ways=5c2*2^3

case 4:ways=5c3*2^2

case 5: ways=5c4*2^1

case 6: ways=5c5*2^0(complete set and null set).

total ways=sum all the six cases.

plz correct if wrong.