Question

for two sets AUB=A iff​

Answer 1

Answer:

if BcA, if b is the subset of A

Answer 2

Answer:

The union of two sets is equal to one set, i.e., $A\cup B=A$ if and only if the set $B$ is a subset or is equal to the set $A$, i.e., $B \subseteq A$.

Step-by-step explanation:

Let us take an example for the given problem,

Let the set $A = \{a,b,c,d,e\}$ and set B can have three possibilities:

Case-1: When sets $B=A$, then $B = \{a,b,c,d,e\}$

So, taking the union of the two sets, we get:

$A\cup B=A=\{a,b,c,d,e\}$

Case-2: When the set B is a subset of A, i.e., $B \subset A$, then let $B=\{ b,c\}$

So, taking the union of the two sets, we get:

$A\cup B=A=\{a,b,c,d,e\}$

Case-3: When the set B has different element than set A, then let $B=\{b,c,f,g\}$,

So, taking the union of the two sets, we get:

$A\cup B=\{a,b,c,d,e,f,g\} \ne A$

Observing the three possibilities, we can easily say that:

$A\cup B=A$  if and only if $B\subseteq A$.