The Problem:
The set T is defined to be all two digit multiples of 2 under 25.
1. How many subsets are there for T?
2. Create a set, V, that is a subset of T.
3. State an element that is in T but not in V.
5 MARKS:
1 mark for showing work in a)
1 mark for correct answer in a)
2 marks for creating a set that is a subset of T
1 mark for correctly identifying an element that is in T but not in V
1. To find the number of subsets for set T, we can use the formula 2^n, where n is the number of elements in the set. In this case, the set T consists of all two-digit multiples of 2 under 25. The two-digit numbers that are multiples of 2 under 25 are 10, 12, 14, 16, 18, 20, 22, and 24. So n = 8.
Using the formula 2^n, the number of subsets for set T is 2^8 = 256.
Answer: There are 256 subsets for set T.
2. Let's create a set V that is a subset of T.
We can choose any combination of the two-digit multiples of 2 under 25 to include in set V. Let's choose the following numbers: 10, 14, 16, and 20.
Set V = {10, 14, 16, 20}
Answer: Set V = {10, 14, 16, 20}
3. To find an element that is in set T but not in set V, we need to find a two-digit multiple of 2 under 25 that is not included in set V.
An element that is in set T but not in set V is 12.
Answer: 12 is an element that is in set T but not in set V.
To solve the given problem, we will follow these steps:
Step 1: Identify the set T
The set T is defined as all two-digit multiples of 2 that are less than 25. Let's list down the elements of T:
T = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Step 2: Determine the number of subsets for T
To find the number of subsets for a set with n elements, we use the formula 2^n. T has 12 elements, so the number of subsets for T can be calculated as:
Number of subsets = 2^12 = 4096
Step 3: Create a subset V of T
To create a subset V of T, we can select any combination of elements from T. Let's create V as:
V = {2, 6, 10, 14, 18}
Step 4: Identify an element that is in T but not in V
From our definition of T and V, we can identify an element that is in T but not in V. Let's pick one:
Element: 4
To summarize:
1. There are 4096 subsets for the set T.
2. A subset V = {2, 6, 10, 14, 18} is created.
3. An element 4 is in T but not in V.