Question

Given A = {Natural numbers less than 10}, B = {Letters of the word PUPPET}, C = {Squares of first four whole numbers} and D = {Odd numbers divisible by 2}. Find $A\cap B$ and $A\cup B$.

Answer 1

We know that the sets are given in descriptive form. So, we must first convert them into tabular form. We also know that the intersection of two sets is the collection of all those elements that occur in both sets. And union of two sets is the combination of all those elements that occur at least once in any of the sets. Hence, we can find the intersection and union of sets A and B.

Complete step-by-step solution:
We can see that all the four sets A, B, C and D are represented in descriptive form. So, let us first change all these sets in tabular form.
We know that in tabular form of set representation, we list all the elements of a set, separated by commas and enclosed within curly brackets {}.
We can see it is given that set A contains natural numbers less than 10.
We know that all counting numbers starting from 1 are called natural numbers. Thus, the list of natural numbers is 1, 2, 3, 4, 5, …
Hene, we can say that, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}.
It is given that set B contains letters of the word PUPPET. Thus, we can say that the set B = {P, U, E, T}.
We can see that set C is the set containing the squares of the first four whole numbers. We know that the first four whole numbers are 0, 1, 2 and 3. So, their squares are 0, 1, 4 and 9.
Thus, we can say that set C = {0, 1, 4, 9}.
It is given that set D contains the odd numbers that are divisible by 2. But we know that no odd number is divisible by 2. Thus, the set D is a null set, or D = $\phi$.
We know that intersection of two sets is the collection of all those elements that occur in both sets.
But we can see that there is no element that occurs both in set A and set B.
So, $A\cap B= \phi$.
We also know that the union of two sets is a combination of all those elements that occur at least once in any of the sets.
Hence, we can say that $A\cup B$= {1, 2, 3, 4, 5, 6, 7, 8, 9, P, U, E, T}.
Thus, $A\cap B=\\{\phi \\}$ and $A\cup B$= {1, 2, 3, 4, 5, 6, 7, 8, 9, P, U, E, T}.

Note: We know that a set which does not contain any element is called an empty set or a null set, and is represented by the Greek symbol $\phi$. We must also remember that a set always contains unique elements and there can be no repeated element in any set.