A set A={x:1 </=x </=3}and B={1,10}are subset of UK ={x:1 </=x </=10},where x is an integer.
Yes, both set A and set B are subsets of set UK.
For set A, all the integers between 1 and 3 (inclusive) are included in set UK. Therefore, set A is a subset of set UK.
For set B, both 1 and 10 are integers that are also included in set UK. Therefore, set B is a subset of set UK.
To determine if sets A and B are subsets of set UK, follow these steps:
Step 1: Define the sets A, B, and UK.
A = {x: 1 ≤ x ≤ 3}
B = {1, 10}
UK = {x: 1 ≤ x ≤ 10}
Step 2: Check if every element of set A is also in set UK.
In set A, the elements are x such that 1 ≤ x ≤ 3.
Checking each element:
For x = 1, we find that 1 is also in set UK.
For x = 2, we find that 2 is also in set UK.
For x = 3, we find that 3 is also in set UK.
Since all the elements of set A are also in set UK, set A is a subset of set UK.
Step 3: Check if every element of set B is also in set UK.
In set B, the elements are 1 and 10.
Checking each element:
For x = 1, we find that 1 is also in set UK.
For x = 10, we find that 10 is also in set UK.
Since all the elements of set B are also in set UK, set B is a subset of set UK.
Conclusion: Both set A and set B are subsets of set UK.