Answer with Step-by-step explanation:
We are given that two sets A and B
[tex]A\subset B[/tex]
We have to prove show that [tex]A\cap B=A\cup B[/tex]
Suppose , x belongs to [tex}A\cap B[/tex]
Then , [tex]x\in A,x\in B[/tex]
Then, [tex]x\in (A\cup B)[/tex]
If, [tex]x\in (A\cup B)[/tex]
Then, [tex]x\in A or x\in B[/tex]
If [tex]x\in B[/tex] Then, it is not necessary that x belongs to A .
If x belongs to A then
[tex]A\cap B=(A\cup B)[/tex]
If x does not belongs to A then
[tex]A\cap B \neq(A\cup B)[/tex]
But, if x belongs to A then x is also belongs to B because A is a subset of B.
Then, [tex]A\cap B=(A\cup B)[/tex]
