Discrete Math 2 10 pts Let A 1 2 and B 23 Find PA PB PA U

Discrete Math

(2) (10 pts) Let A = (1, 2} and B = (2,3}. Find P(A), P(B), P(A) U P(B) and P(A U B). What is your conjecture about the relation between P(A) U P(B) and P(A U B)?

Solution

Number of element in A is 2,

Number of element in B is 2,

Total number of element present is (2+2)=4,

P(A) = (Number of element in A)/(Total number of element) = (2/4) = 1/2

P(B) = (Number of element in B)/(Total number of element) = (2/4) = 1/2

P(A intersection B)= (Number of element common in A and B)/(Total number of element) = 1/4

P(A) union P(B) = P(A)+P(B) = 1/2+1/2 = 1
P(A union B) = P(A) + P(B) - P(A intersection B) = 1/2 + 1/2 - 1/4 =3/4

and P(A union B) = (P(A) Union P(B)) - (P(A intersection B))