Let Y = {1, 2, 3, 4, 5}, A = {1, 2}, B = {3, 4, 5} and denotes null set. If (A × B) denotes Cartesian product of the sets A and B, then (Y × A) ? (Y × B) is

Question

Let Y = {1, 2, 3, 4, 5}, A = {1, 2}, B = {3, 4, 5} and $ϕ$ denotes null set. If (A × B) denotes Cartesian product of the sets A and B, then (Y × A) ∩ (Y × B) is

Smart Achievers · Accepted Answer

(4)

$Y \times A = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2), (5, 1), (5, 2)}$

$Y \times B = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5), (4, 3), (4, 4), (4, 5), (5, 3), (5, 4), (5, 5)}$

$∴$ $(Y \times A) \cap (Y \times B) = ϕ$

Solution

Q.
Let Y = {1, 2, 3, 4, 5}, A = {1, 2}, B = {3, 4, 5} and $ϕ$ denotes null set. If (A × B) denotes Cartesian product of the sets A and B, then (Y × A) ∩ (Y × B) is

1 Y

2 A

3 B

4 $ϕ$

Ans.
(4)

$Y \times A = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2), (5, 1), (5, 2)}$

$Y \times B = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5), (4, 3), (4, 4), (4, 5), (5, 3), (5, 4), (5, 5)}$

$∴$ $(Y \times A) \cap (Y \times B) = ϕ$

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Solution

Q. Let Y = {1, 2, 3, 4, 5}, A = {1, 2}, B = {3, 4, 5} and ϕ denotes null set. If (A × B) denotes Cartesian product of the sets A and B, then (Y × A) ∩ (Y × B) is

1 Y

2 A

3 B

4 ϕ

Ans. (4) Y×A={(1,1),(1,2),(2,1),(2,2),(3,1),(3,2),(4,1),(4,2),(5,1),(5,2)} Y×B={(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,3),(3,4),(3,5),(4,3),(4,4),(4,5),(5,3),(5,4),(5,5)} ∴ (Y×A)∩(Y×B)=ϕ

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Q.
Let Y = {1, 2, 3, 4, 5}, A = {1, 2}, B = {3, 4, 5} and $ϕ$ denotes null set. If (A × B) denotes Cartesian product of the sets A and B, then (Y × A) ∩ (Y × B) is

4 $ϕ$

Ans.
(4)

$Y \times A = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2), (5, 1), (5, 2)}$

$Y \times B = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5), (4, 3), (4, 4), (4, 5), (5, 3), (5, 4), (5, 5)}$

$∴$ $(Y \times A) \cap (Y \times B) = ϕ$