Question

GE 3 of 5 In #3, are the sets Band D disjoint? Why or why not? BE ECITUSE 3 are 3 pts. Cormon +3 Snce they have Suppose that, in a 7 ounce bag of M&Ms Candy, there are 220 pieces of candy. If 20 pieces red or blue? are red and 53 pieces are blue, how many pieces are some other color than either A EvEuRO Peses B= Ex Euls3 ices care blue ar Re 220-20-53- 147 14 5 pts. Lhi-(,0U V) 87, et A and Bbe subsets of a universal set U and suppose that n(U) = 350, n(A) 109 and n(AU B) 192. Then how many elements are in A n B? (B) 105 97103

check problem 4 and 5 please

Answer 1

(4)

Let A be the set of all red elements.

n (A) =20

Let B be the set of all blue elements.

n (B)53

Total number of candies $=220$

That is

n(U)220

$U\rightarrow$ Universal set.

A and B are disjoint sets.Since A and B does not have common elements.

n (An B)= 0

Number of pieces which have color other than either blue or red is given by

(Acn B n (AU B)

n (U)- n (AUB)

n (U)n (A)+n (B)-n (An B)

=220 2053 0

$=147$

That is

Number of pieces which are neither blue nor red is $\boldsymbol{=147}$

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(5)

$n\left ( A \right )=87$

n (B) 109

$n\left ( A\cup B \right )=192$

$n\left ( A\cup B \right )=n\left ( A \right )+n\left ( B \right )-n\left ( A\cap B \right )$

$n\left ( A\cap B \right )=n\left ( A \right )+n\left ( B \right )-n\left ( A\cup B \right )$

$=87+109-192$

$=4$

That is

$\boldsymbol{n\left ( A\cap B \right )=4}$

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