If A ⊂ B, then A ∩ B = A ∪ B.

Question

asked May 16, 2019 177k views

2 Answers

Brice Rebsamen · Answer 1 · 2019-05-21T08:58:35+0000

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

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

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

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