Question

If A B are finite sets such that A={x y z} B={1 2} then A times B is the cartesian product such that n(A times B)=a and C is the power set of A such that n(C)=c .Number of relations on B itself is b number of subsets of B is d then a+b+c+d=
OPTIONS:16,36,34,35​

Answer 1

Answer:

let the number of elements in A be m and B be n

therefore the total number of subsets of A is 2

m

and number of subsets of B is 2

n

given 2

m

−2

n

=960

we know from this equation that m>n

therefore taking n common we get

2

n

(2

m−n

−1)=960

as 2

(

m−n)−1 is odd the even part is only 2

n

960 can be written as 2

6

×15

therefore from above equation we can observe that n=5

and $$2^(m-5)-1$=15$

⇒2

(

m−5)=16 so m=9

therefore n(A)-n(B)=m-n=4

Step-by-step explanation:

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