Math, asked by monjyotiboro, 3 months ago

For any two sets A and B prove that...
A is a subset of A union B.​

Answers

Answered by priyappu55
0

∵ A∩B is set of all that elements that belongs to both A and B. Hence, all elements of A∩B contained in A.

Hence,

A∩B⊂A

Answered by user0888
9

Answer Keys.

This is an identity. The explanation is as follows.

Solution.

Using the Benn diagram,

  • A\cup B is the grey region.
  • A is the yellow region.

Hence, A belongs to the region of A\cup B. In other words, A\subset (A\cup B).

More information.

Proof by Contrapositive

Sets are one of the ways that are used in proofs. Let's take an example.

How do we prove, that for x, y such that x+y\neq 5 the values are \mathrm{x\neq 2\;or\;y\neq 3}?

At the first glance, this looks complicated, but it is easier to solve with sets.

\mathrm{p:x+y\neq5}, \mathrm{q:x\neq2\;or\;y\neq3}

Let the truth sets of two statements be \mathrm{P} and \mathrm{Q}. We need P\subset Q. If the statement is true, Q^C\subset P^C will be true according to the Benn diagram.

We shall test \sim q\rightarrow \sim p. Now given statement becomes "for the values of x, y such that \mathrm{x= 2\;and\;y= 3} we have \mathrm{x+y= 5}."

It is true, and this way of proof is proof by contrapositive.

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