Question

if A U B =B then show that A is contained in B​

Answer 1

Step-by-step explanation:

hope this helps you this is ur answer

Answer 2

Let,

$\displaystyle\longrightarrow\sf{x\in (A\cup B)}$

$\displaystyle\longrightarrow\sf{x\in A\lor x\in B}$

But since $\displaystyle\sf{A\cup B=B,\ x}$ must be an element in B.

That means,

p : It is necessary that $\displaystyle\sf {x\in B}$ even though $\displaystyle\sf{x\in A,}$ and hence we can say that $\displaystyle\sf {A\subseteq B.}$

q : If $\displaystyle\sf {x\in (B-A),}$ it must also be included in B as $\displaystyle\sf {(B-A)\subseteq B,}$ but this does not say whether $\displaystyle\sf {A\subseteq B}$ is true.

Hence the statement 'p' proves the condition.

QED