Question

question 2 of 5 select the correct answer. preston purchased a new briefcase that has a 3 - digit combination lock, where no two digits can be the same, and the digits can range from 0 to 5. let event a be setting a combination such that all the digits are odd. let event b be setting an odd number greater than 500 as the combination. which of the following outcomes represents the union of a and b? {135, 153, 315, 351, 513, 531, 501, 503, 521, 523, 541, 543} {135, 153, 315, 351, 513, 531} {501, 503, 513, 521, 523, 531, 541, 543} {513, 531}

Explanation:

Step1: Analyze event A

Event A has combinations with all - odd digits. The odd digits in the range 0 - 5 are 1, 3, 5.

Step2: Analyze event B

Event B has odd - numbered combinations greater than 500. The first digit for a number greater than 500 from the given range can be 5.

Step3: Find the union

The union of A and B will contain all combinations that are either all - odd digit combinations or odd - numbered combinations greater than 500.
The all - odd digit combinations are made up of 1, 3, 5. The odd - numbered combinations greater than 500 can start with 5 and have odd digits in the remaining places.
The set of all such combinations is {135, 153, 315, 351, 501, 503, 513, 521, 523, 531, 541, 543}

Answer:

{135, 153, 315, 351, 501, 503, 513, 521, 523, 531, 541, 543}