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Standard XII

Mathematics

Difference of Two Sets

If A = x ∶ x ...

Question

If $A = {x ∶ x is a multiple of 3}$ and $B = {x ∶ x is a multiple of 5}$ , then $A - B =$

A^{C} \cap B

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A \cap B^{C}

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A^{C} \cap B^{C}

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(A \cap B)^{C}

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Solution

The correct option is B $A \cap B^{C}$
$A - B = A - A \cap B$
$A \cap B = {x : x is a multiple of 15}$
Let $S$ be the universal set.
Then $A \cap S = A$
$∴ A - A \cap B = A \cap S - A \cap B = A \cap (S - B) = A \cap B^{C}$

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Similar questions

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

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 $A \subset C$

(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 $x \notin A .$

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

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

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

(i)

x \in A

and

A \in B

, then

x \in B

(i i)

A \subset B

and

B \in C

, then

A \in C

(i i i)

A \subset B

and

B \subset C

, then

A \subset C

(i v)

A \subset̸ B

and

B \subset̸ C

, then

A \subset̸ C

(v)

x \in A

and

A \subset̸ B

, then

x \in B

(v i)

A \subset B

and

x \notin B

, then

x \notin A

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If A={x∶x is a multiple of 3} and B={x∶x is a multiple of 5}, then A−B=

The correct option is B A∩BCA−B=A−A∩B A∩B={x:x is a multiple of 15} Let S be the universal set. Then A∩S=A ∴A−A∩B=A∩S−A∩B=A∩(S−B)=A∩BC

If $A = {x ∶ x is a multiple of 3}$ and $B = {x ∶ x is a multiple of 5}$ , then $A - B =$

The correct option is B $A \cap B^{C}$
$A - B = A - A \cap B$
$A \cap B = {x : x is a multiple of 15}$
Let $S$ be the universal set.
Then $A \cap S = A$
$∴ A - A \cap B = A \cap S - A \cap B = A \cap (S - B) = A \cap B^{C}$