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Byju's Answer

Standard VIII

Mathematics

Intersection of Sets

If A ⋂ B = B,...

Question

$I f A ⋂ B = B, t h e n$

$A \subset B$

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$B \subset A$

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$A = ɸ$

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$B = ɸ$

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Solution

The correct option is B
$B \subset A$

Explanation for the correct option:
Given, $A \cap B = B$
Which means elements of are in the both sets $A$ and $B$
All the elements of are contained in the intersection of $A$ and $B$ which is equal to $B$ .
$B \subset A$
Hence, option(B) is correct.

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Similar questions

State, Whether the following statements are true of false.

(i) If $a < b, t h e n a - c < b - c$

(ii) If $a > b, t h e n a + c > b + c$

(iii) If $a < b, t h e n a c > b c$

(iv) If $a > b, t h e n \frac{a}{c} < \frac{b}{c}$

(v) If $a - c > b - d; t h e n a + d > b + c$

(vi) If $a < b, a n d c > 0, t h e n a - c > b - c where a, b, c and are real numbers and c \neq 0.$

Q. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
(i) If

x \in A

and

A \in B

, then

x \in B

(ii) If

A \subset B

and

B \in C

, then

A \in C

(iii) If

A \subset B

and

B \subset C

, then

A C

(iv) If

A \subset̸ B

and

B \subset̸ C

, then

A \subset̸ C

(v) If

x \in A

and

A \subset̸ B

, then

x \in B

(vi) If

A \subset B

and

x \notin B

, then

x \notin A

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

(i) If x ∈ A and A ∈ B, then x ∈ B

(ii) If A ⊂ B and B ∈ C, then A ∈ C

(iii) If A ⊂ B and B ⊂ C, then A ⊂ C

(iv) If A ⊄ B and B ⊄ C, then A ⊄ C

(v) If x ∈ A and A ⊄ B, then x ∈ B

(vi) If A ⊂ B and x ∉ B, then x ∉ A

Q. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x ∈ A and A ∈ B, then x ∈ B (ii) If A ⊂ B and B ∈ C, then A ∈ C (iii) If A ⊂ B and B ⊂ C, then A ⊂ C (iv) If A ⊄ B and B ⊄ C, then A ⊄ C (v) If x ∈ A and A ⊄ B, then x ∈ B (vi) If A ⊂ B and x ∉ B, then x ∉ A

P (A - B) = P (A) - P (A ⋂ B) = P (A ⋃ B) - P (B) = P (A ⋂ ¯ B) = 1 - P (¯ A ⋂ B)

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IfA⋂B=B,then

The correct option is B B⊂AExplanation for the correct option:Given,A∩B=B Which means elements of are in the both sets A and BAll the elements of are contained in the intersection of Aand B which is equal to B.B⊂AHence, option(B) is correct.

$I f A ⋂ B = B, t h e n$

The correct option is B
$B \subset A$

Explanation for the correct option:
Given, $A \cap B = B$
Which means elements of are in the both sets $A$ and $B$
All the elements of are contained in the intersection of $A$ and $B$ which is equal to $B$ .
$B \subset A$
Hence, option(B) is correct.