QBManager

Sets, Relation and Function

116781 If $A = {a, b, c}, B = {b, c, d}$ and $C = {a, d, c}$ , then $(A - B) \times (B \cap C) =$

1

{(a, c), (a, d)}

2

{(a, b), (c, d)}

3

{(c, a), (d, a)}

4

{(a, c), (a, d), (b, d)}

Explanation:

A Given, $A = {a, b, c} B = {b, c, d}$ and $c = {a, d, c}$
Then, $A - B = {a, b, c} - {b, c, d}$
$A - B = {a}$
and, $B \cap C = {b, c, d} \cap {a, d, c}$
$B \cap C = {d, c}$
So, $(A - B) \times (B \cap C) = {a} \times {d, c} = {a} \times {c, d}$ .
$(A - B) \times (B \cap C) = {(a, c), (a, d)} .$

Karnataka CET 2006

Sets, Relation and Function

116777 If $A$ and $B$ be two sets such that $A \times B$ consists of 6 elements. If three elements $A \times B$ are $(1, 4)$ $(2, 6)$ and $(3, 6)$ , find $B \times A$ .

1

{(1, 4), (1, 6), (2, 4), (2, 6), (3, 4), (3, 6)}

2

{(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}

3

{(4, 4), (6, 6)}

4

{(4, 1), (6, 2) \cdot (6, 3)}

Explanation:

Given, A and B be two sets.
And $(1, 4), (2, 6)$ and $(3, 6)$ are the elements of $A \times B$
Then by ordered pair 1, 2, 3 are the elements of $A$ and 4,6 are the elements of $B$ .
$∴ A = {1, 2, 3}, B = {4, 6}$ So, $B \times A = {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}$
Ans:
Exp:

VITEEE-2011

Sets, Relation and Function

116778 If $A$ and $B$ have $n$ elements in common, then the number of elements common to $A \times B$ and $B \times A$ is

1 0

2

n

3

2 n

4

n^{2}

Explanation:

D Given, A and B have $n$ elements in common. So, the number of elements common to $A \times B$ and $B \times A$ is
$n \times n = n^{2}$

Karnataka CET 2012

Sets, Relation and Function

116781 If $A = {a, b, c}, B = {b, c, d}$ and $C = {a, d, c}$ , then $(A - B) \times (B \cap C) =$

1

{(a, c), (a, d)}

2

{(a, b), (c, d)}

3

{(c, a), (d, a)}

4

{(a, c), (a, d), (b, d)}

Explanation:

A Given, $A = {a, b, c} B = {b, c, d}$ and $c = {a, d, c}$
Then, $A - B = {a, b, c} - {b, c, d}$
$A - B = {a}$
and, $B \cap C = {b, c, d} \cap {a, d, c}$
$B \cap C = {d, c}$
So, $(A - B) \times (B \cap C) = {a} \times {d, c} = {a} \times {c, d}$ .
$(A - B) \times (B \cap C) = {(a, c), (a, d)} .$

Karnataka CET 2006

Sets, Relation and Function

116777 If $A$ and $B$ be two sets such that $A \times B$ consists of 6 elements. If three elements $A \times B$ are $(1, 4)$ $(2, 6)$ and $(3, 6)$ , find $B \times A$ .

1

{(1, 4), (1, 6), (2, 4), (2, 6), (3, 4), (3, 6)}

2

{(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}

3

{(4, 4), (6, 6)}

4

{(4, 1), (6, 2) \cdot (6, 3)}

Explanation:

Given, A and B be two sets.
And $(1, 4), (2, 6)$ and $(3, 6)$ are the elements of $A \times B$
Then by ordered pair 1, 2, 3 are the elements of $A$ and 4,6 are the elements of $B$ .
$∴ A = {1, 2, 3}, B = {4, 6}$ So, $B \times A = {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}$
Ans:
Exp:

VITEEE-2011

Sets, Relation and Function

116778 If $A$ and $B$ have $n$ elements in common, then the number of elements common to $A \times B$ and $B \times A$ is

1 0

2

n

3

2 n

4

n^{2}

Explanation:

D Given, A and B have $n$ elements in common. So, the number of elements common to $A \times B$ and $B \times A$ is
$n \times n = n^{2}$

Karnataka CET 2012

Sets, Relation and Function

116781 If $A = {a, b, c}, B = {b, c, d}$ and $C = {a, d, c}$ , then $(A - B) \times (B \cap C) =$

1

{(a, c), (a, d)}

2

{(a, b), (c, d)}

3

{(c, a), (d, a)}

4

{(a, c), (a, d), (b, d)}

Explanation:

A Given, $A = {a, b, c} B = {b, c, d}$ and $c = {a, d, c}$
Then, $A - B = {a, b, c} - {b, c, d}$
$A - B = {a}$
and, $B \cap C = {b, c, d} \cap {a, d, c}$
$B \cap C = {d, c}$
So, $(A - B) \times (B \cap C) = {a} \times {d, c} = {a} \times {c, d}$ .
$(A - B) \times (B \cap C) = {(a, c), (a, d)} .$

Karnataka CET 2006

Sets, Relation and Function

116777 If $A$ and $B$ be two sets such that $A \times B$ consists of 6 elements. If three elements $A \times B$ are $(1, 4)$ $(2, 6)$ and $(3, 6)$ , find $B \times A$ .

1

{(1, 4), (1, 6), (2, 4), (2, 6), (3, 4), (3, 6)}

2

{(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}

3

{(4, 4), (6, 6)}

4

{(4, 1), (6, 2) \cdot (6, 3)}

Explanation:

Given, A and B be two sets.
And $(1, 4), (2, 6)$ and $(3, 6)$ are the elements of $A \times B$
Then by ordered pair 1, 2, 3 are the elements of $A$ and 4,6 are the elements of $B$ .
$∴ A = {1, 2, 3}, B = {4, 6}$ So, $B \times A = {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}$
Ans:
Exp:

VITEEE-2011

Sets, Relation and Function

116778 If $A$ and $B$ have $n$ elements in common, then the number of elements common to $A \times B$ and $B \times A$ is

1 0

2

n

3

2 n

4

n^{2}

Explanation:

D Given, A and B have $n$ elements in common. So, the number of elements common to $A \times B$ and $B \times A$ is
$n \times n = n^{2}$

Karnataka CET 2012

Explanation:

Explanation:

Explanation:

Question Bank Series

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation: