How do i solve this -given that p and q are sets of real numbers such that p=(x:0 is lesser than or equal to x is lesser than or equal to 3)and q=(x:3 is lesser than x is lesser than 2),find p union q
pUq = (0 <= x <= 3) U (3 < x < 2) = [0,3] U Ø = [0,3]
There is no number greater than 3 and less than 2
To find the union of sets p and q, you need to combine all the elements from both sets without duplicates.
Given that p = {x: 0 ≤ x ≤ 3} and q = {x: 3 < x < 2}, let's solve this step by step.
Step 1: List the elements of set p:
Since p represents the set of real numbers x such that 0 ≤ x ≤ 3, we can list the elements in set p as:
p = {0, 1, 2, 3}
Step 2: List the elements of set q:
Since q represents the set of real numbers x such that 3 < x < 2, we see that there are no numbers that satisfy this condition. Hence, set q is an empty set: q = {}
Step 3: Find the union of sets p and q:
The union of two sets, p and q, denoted as p ∪ q, is the set that contains all elements from both sets without duplicates.
Since set q is an empty set (i.e., it does not contain any elements), the union of p and q will be equal to set p itself:
p ∪ q = {0, 1, 2, 3}
Therefore, the union of sets p and q is {0, 1, 2, 3}.
To find the union of two sets, we need to combine all the elements from both sets without any repetition. In this case, we have two sets p and q, defined as follows:
p = {x: 0 ≤ x ≤ 3}
q = {x: 3 < x < 2}
To find the union of p and q, we need to combine all the elements from both sets.
Let's start with set p:
p = {x: 0 ≤ x ≤ 3}
This set includes all values of x that are greater than or equal to 0 and less than or equal to 3. Visualizing this on a number line, we can see that it includes all values between 0 and 3, including 0 and 3 themselves.
Next, let's look at set q:
q = {x: 3 < x < 2}
This set includes all values of x that are greater than 3 and less than 2. However, this is an empty set because there are no values of x that satisfy this condition. The inequality 3 < x < 2 cannot be true since 3 is not less than 2.
Now, to find the union of p and q, we need to combine all the elements from both sets without any repetition. Since q is an empty set, the union of p and q will be the same as set p.
Therefore, p union q = {x: 0 ≤ x ≤ 3}