From the given information, we can infer that at least some fruits are vegetables, and some vegetables are red. Therefore, it must be true that some fruits are red.

The minimum number of students in the group is the sum of students who like mathematics and those who like science, minus the number of students who like both subjects. So, 20+15−10 = 25 Since every student likes at least one subject, the minimum number of students is 25 + 10 = 35.

If Alice is not the tallest, then someone else in the group must be taller than Alice. Since Bob is taller than Carol and Carol is taller than David, David must be the shortest in the group.

Let's analyze the given series: {11, A, 23, B, C, 68, 73}. The median of a series is the middle value when the values are arranged in ascending order. In this case, the series is already in increasing order: {11, A, 23, B, C, 68, 73} Now, if half the range is equal to the median, we need to find the range and divide it by 2. Range = Largest value - Smallest value In this series, the largest value is 73, and the smallest value is 11. Range = 73 - 11 = 62 Half the range = 62 / 2 = 31 Now, we need to find the element in the series that is 31 units away from the smallest value (11). Counting 31 units from 11, we get: 11 + 31 = 42 So, the element with the value 42 is the median of the series. Therefore, the median of the series {11, A, 23, B, C, 68, 73} is 42.