Mathematics: Use use an element argument to prove the state (a-b)u(anb) = a is true. he statement for all sets a and b,

Use use an element argument to prove the state

Tf0273433

14.03.2022

Answer with Step-by-step explanation:

We have to prove that

$(A-B)\cup (A\cap B)=A$ is true for all sets A and B

Let $x\in(A-B)\cup (A\cap B)$

Then $x\in(A-B)$ or $x\in(A\cap B)$

$x\in A$ and $x\notin B$ or $x\in A\;and\; x\in B$

Hence, $x\in A$

Conversely ,Let $x\in A$

Then x belongs to A and x does not belongs to B then

x belongs to A- B

Or x belongs to A and x belongs to B then x belongs to $A \cap B$

Hence, $x\in( A-B)\cup (A\cap B)$

Therefore, $(A-B)\cup (A\cap B)=A$

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kush3489t

11.08.2022

uhh why are you racist I'll never know

Step-by-step explanation:

you have no business asking this question it offends people and its rude

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