Question

Prove n(AnB') + n(AnB) = n(A) Will mark brainliest

Answer 1

let,

U={1,2,3,4,5,6,7,8,9}

A={1,2,3}

B={5,6}

now,

B'

=U-B

={1,2,3,4,5,6,7,8,9}-{5,6}

={{1,2,3,4,7,8,9}

now,

AnB'

={1,2,3}n{1,2,3,4,7,8,9}

={1,2,3}

here,

n(AnB')=3

again,

AnB

={1,2,3}n{5,6}

={1,2,3,5,6}

n(AnB)=6

now,

n(AnB')+n(AnB)=3+6=9

n(A)=3

so they are not equal.....

Answer 2

Answer:

n(a)=No. of objects in

an(b)=No. of objects in banb contains objects common between sets a and b

Now, n(a)+n(b) contains total number of objects in a and b including those which are common to a as well as b.

Which means, those objects are counted twice as they constitute both a and b.

So, to exclude them, such that we count all the objects in a and b only once,

we write…n(a)+n(b)-n(anb)

But the above sentence is the definition of n(aub).

Therefore, n(aub)=n(a)+n(b)-n(anb)