a number cube has faces numbered 1 to 6. what is true about rolling the number cube one time? select three…

a number cube has faces numbered 1 to 6. what is true about rolling the number cube one time? select three options. □s = {1, 2, 3, 4, 5, 6} □if a is a subset of s, a could be {0, 1, 2}. □if a is a subset of s, a could be {5, 6}. □if a subset a represents the complement of rolling a 5, then a = {1, 2, 3, 4, 6}. □if a subset a represents the complement of rolling an even number, then a = {1, 3}.

a number cube has faces numbered 1 to 6. what is true about rolling the number cube one time? select three options. □s = {1, 2, 3, 4, 5, 6} □if a is a subset of s, a could be {0, 1, 2}. □if a is a subset of s, a could be {5, 6}. □if a subset a represents the complement of rolling a 5, then a = {1, 2, 3, 4, 6}. □if a subset a represents the complement of rolling an even number, then a = {1, 3}.

Answer

Answer:

  1. S = {1, 2, 3, 4, 5, 6}
  2. If A is a subset of S, A could be {5, 6}
  3. If a subset A represents the complement of rolling a 5, then A = {1, 2, 3, 4, 6}

Explanation:

Step1: Define sample - space

The sample - space S of rolling a number cube numbered 1 to 6 is all possible outcomes, so S = {1, 2, 3, 4, 5, 6}.

Step2: Check subset condition

A subset of S must have elements that are in S. Since 0 is not in S, {0, 1, 2} cannot be a subset of S. But {5, 6} has elements from S, so it can be a subset of S.

Step3: Find complement

The complement of rolling a 5 means all outcomes that are not 5. So A = {1, 2, 3, 4, 6}.

Step4: Check complement of even numbers

The set of even numbers on the cube is {2, 4, 6}. The complement should be {1, 3, 5}, not {1, 3}.