If A={5x/x belongs to Z,x less than or equal to 30} B={x/x is a prime number;1 less than or equal to x less than or equal to 25}verify whether A and B are disjoint or intersecting sets.
well, just list the elements of A and B:
A = {...-15,-10,-5,0,5,10,15,...,150}
B = {2,3,5,7,11,13,17,19,23}
so, what do you think?
I suspect you really meant
A = {x|x ε N, x≤30}
since those are the positive integers
To verify whether sets A and B are disjoint or intersecting, we need to check if they have any elements in common. Let's follow the steps below to determine this:
1. Find the elements in set A:
Set A is defined as A = {5x / x belongs to Z, x ≤ 30}. Here Z represents the set of integers.
To find the elements in set A, we substitute values from the set of integers (Z) into the expression 5x and check if the result is less than or equal to 30.
Let's calculate some values of A:
For x = 0, A = 5(0) = 0.
For x = 1, A = 5(1) = 5.
For x = -1, A = 5(-1) = -5.
For x = 2, A = 5(2) = 10.
Similarly, we can calculate values of A for other integers up to x = 30.
2. Find the elements in set B:
Set B is defined as B = {x / x is a prime number; 1 ≤ x ≤ 25}.
To find the elements in set B, we list all the prime numbers between 1 and 25.
Prime numbers between 1 and 25 are: 2, 3, 5, 7, 11, 13, 17, 19, 23.
3. Compare the elements in sets A and B:
By comparing the elements in sets A and B, we can determine if they have any common elements.
Looking at the elements in set A and set B, we can observe that the number 5 is present in both sets. So, there is at least one element that is common to both sets.
4. Conclusion:
Since sets A and B have at least one common element (which is 5), the sets A and B are intersecting sets.