Question

Let $A = \\{ a,b\\}$ and $B = \\{ a,b,c\\}$. Is $A \subset B$ ? What is $A \cup B$ ?

Answer 1

Here we must know what the symbol means and how it relates A and B. This symbol means whether A is the subset of B which is symbolised as $A \subset B$ and also we can say it in the other terms which says all the elements of set $A$ are contained in set B. If all the elements of the set $A$ are contained in the set B then we can say that $A \subset B$
And $A \cup B$ means which consists of all the elements of $A{\text{ and }}B$ and we need to find it.

Complete step-by-step answer:
Here we are given the two sets which are set A and set B. The set A contains $2$ elements and set B contains $3$ elements as:
$A = \\{ a,b\\}$, $B = \\{ a,b,c\\}$
And we are asked whether $A \subset B$ which means whether $A$ is the subset of $B$ or not. Here we must know what the symbol means and how it relates A and B. This symbol means whether A is the subset of B which is symbolised as $A \subset B$ and also we can say it in the other terms which says all the elements of set $A$ are contained in set B. if all the elements of the set $A$are contained in the set B then we can say that $A \subset B$
So as we see that$A = \\{ a,b\\}$, $B = \\{ a,b,c\\}$
Here we notice that all the elements which are in the set A that is $a,b$ are also present in the set $B$
So we can say that A is the subset of B. Hence $A \subset B$
Now we need to find the $A \cup B$
Here we need to find what $A \cup B$ will contain. The $A \cup B$ means the union of all the elements of the set $A$ and the set B. Here in $A \cup B$ all the elements of set A and set B must be present. If any term is in both the sets then we need to count it only once.
So we know that$A = \\{ a,b\\}$, $B = \\{ a,b,c\\}$
Hence we can say $A \cup B = \\{ a,b,c\\}$

Note: In these kinds of questions we must know what the symbols that relate the two sets represent and symbolises.
For example: $A \cup B$ represents the union of the two sets A and B
The $A \cap B$ means the intersection of the two sets which means the common elements of A and B
The $A \subset B$ means the A is subset of B
Hence in this way we must have the complete knowledge of the symbols’ representation.