Question

If A ⊂ B, then A ∩ B = A ∪ B.

Answer 1

You can illustrate this with a Venn diagram

Answer 2

Answer with Step-by-step explanation:

We are given that two sets  A and B

$A\subset B$

We have to prove show that $A\cap B=A\cup B$

Suppose , x belongs to [tex}A\cap B[/tex]

Then , $x\in A,x\in B$

Then, $x\in (A\cup B)$

If, $x\in (A\cup B)$

Then, $x\in A or x\in B$

If $x\in B$ Then, it is not necessary that x belongs to  A .

If x belongs to A then

$A\cap B=(A\cup B)$

If x does not belongs to A then

$A\cap B \neq(A\cup B)$

But, if x belongs to A then x is also belongs to B because  A is a subset  of B.

Then, $A\cap B=(A\cup B)$