If U = {x : x is an integer and 1 ≤ x ≤ } E1 = {x: x is a multiple of 3} E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the ...

To find the probability that an integer randomly picked from U is not in E2, we need to find the number of integers in U that are not in E2 and divide it by the total number of integers in U. First, let's find the number of integers in U that are not in E2. We can do this by finding the complement of E2 in U, which is the set of integers in U that are not in E2. Since E2 is the set of multiples of 4 in U, we can write the complement of E2 as the set of integers in U that are not multiples of 4. We can express this set using set-builder notation as follows: U \ E2 = {x : x is an integer and x is not a multiple of 4} To find the number of integers in this set, we can count the number of integers in U that are multiples of 4 and subtract it from the total number of integers in U. The largest integer in U that is a multiple of 4 is 99996, which we can find by dividing 100000 by 4 and taking the floor. Therefore, the number of integers in U that are multiples of 4 is: floor(100000/4) = 25000 Since U contains all integers from 1 to 100000, the total number of integers in U is: 100000 - 1 + 1 = 100000 Therefore, the number of integers in U that are not in E2 is: 100000 - 25000 = 75000 To find the probability that an integer randomly picked from U is not in E2, we divide the number of integers in U that are not in E2 by the total number of integers in U: 75000/100000 = 0.75 So the probability that an integer randomly picked from U is not in E2 is 0.75 or 75%. Answer: The correct option is not provided in the question.