Question

If A and B are two non empty sets then AՍB = AՈB iff

(a) ⊂ (b) ⊂ (c) A = B (d) none of these.​

Answer 1

Given : A and B are two non empty sets  

AՍB = AՈB

To Find : AՍB = AՈB iff

A ⊂ B  

B ⊂ A

A = B

None of these

Solution:

A ⊂ B

=> AՍB  = B

   AՈB  =  A

AՍB ≠  AՈB

B ⊂ A

=> AՍB  = A

   AՈB  =  B

AՍB ≠  AՈB

A =  B

=> AՍB  = A = B

   AՈB  =  A = B

   AՍB =  AՈB

AՍB = AՈB  iff A = B

Learn More:

If A and B are sets then find A ∩ ( B ∪ A ) c from the given Venn ...

https://brainly.in/question/25604174

Symbols , #,/ and ? mean the following:A-B means A plus B.A# B ...

https://brainly.in/question/14870099

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If A and B are two non empty sets then A ∪ B = A ∩ B iff

(a) A ⊂ B

(b) B ⊂ A

(c) A = B

(d) None of these

EVALUATION

We will show that If A and B are two non empty sets then A ∪ B = A ∩ B iff A = B

First suppose that A and B are two non empty sets such that A ∪ B = A ∩ B

$\sf{Let \: \: x \: \in \: A}$

$\implies \sf{ x \: \in \: A \: \cup \: B}$

$\implies \sf{ x \in A \cap \: B} \: \: ( \because A \cup \: B = A \cap \: B)$

$\implies \sf{x \in \: B}$

$\therefore \: \: \sf{ A \: \subset \: B} \: \: .....(1)$

Again suppose that

$\sf{ y \: \in \: \: B}$

$\implies \sf{ y \: \in \: A \: \cup \: B}$

$\implies \sf{ y \in A \cap \: B} \: \: ( \because A \cup \: B = A \cap \: B)$

$\implies \sf{ y \in \: A}$

$\therefore \: \sf{B \: \subset \: A} \: \: \: ....(2)$

Hence from (1) & (2)

$\sf{A = B}$

Next suppose that A = B

Then

A ∪ B = B

A ∩ B = B

∴ A ∪ B = A ∩ B

Hence A ∪ B = A ∩ B iff A = B

FINAL ANSWER

If A and B are two non empty sets then A ∪ B = A ∩ B iff

(c) A = B

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If A and B are two sets then A-B =B-A if

https://brainly.in/question/28848928

2. If A is a set of vowels and B is a set of first five natural numbers then

A and B are comparable sets

A and B are equal

https://brainly.in/question/28851425