If P=`{5,6,8,10,12,} , Q = {0,3,6,9,12,15,8} and R = { 0,1,2,3, ….10 }`
`Q cap R `

Answer

To find the intersection of sets Q and R, we will follow these steps:

### Step 1: Identify the elements in each set.
- Set Q = {0, 3, 6, 9, 12, 15, 8}
- Set R = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

### Step 2: List the elements of both sets.
- Elements of Q: 0, 3, 6, 9, 12, 15, 8
- Elements of R: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

### Step 3: Find the common elements between Q and R.
We will check each element in set Q to see if it is also in set R:
- 0 is in R.
- 3 is in R.
- 6 is in R.
- 9 is in R.
- 12 is not in R.
- 15 is not in R.
- 8 is in R.

### Step 4: Compile the common elements.
The common elements between Q and R are: 0, 3, 6, 8, and 9.

### Step 5: Write the intersection of Q and R.
Thus, the intersection of Q and R, denoted as Q ∩ R, is:
Q ∩ R = {0, 3, 6, 8, 9}