Let the universal set, s, have 66 elements. a and b are subsets of s. set a contains 19 elements and set b contains 34 elements. if sets a and b have 10 elements in common, how many elements are in neither a nor b?

The cardinality of the union between two sets is given by

In fact, if an element is in both A and B, it is counted in both N(A) and N(B), so we're counting it twice. By subtracting the cardinality of the interserction, we're taking back one of these "extra-counted" element, and the count is correct. In your case, the numbers are

This means that the two sets cover, without repetitions, 43 of the 66 elements in the sets. So, there are

elements which are in neither A nor B

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet