Let A - y - y -log 2 x - x -16- x - y - N - B - x - x 2-7 x -12-0 then A - B - A - B isA- 3-3B- 1-3-2-3-3-3-4-3- 1-3-2-3-3-3D- 1-3-2-3-3-3-1-4-2-4-3-4

The correct option is B {(1, 3), (2, 3), (3, 3), (4, 3)}A = {y:y=log_2x,x lt;16,x,y∈ℕ} for x lt;16⇒log_2x lt;4 ∴ y∈( ∞,4) & y∈ℕ ∴ A={1,2,3} B={x:x^2 ...

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Byju's Answer

Standard XII

Mathematics

Ordered Pair

Let A = y : y...

Question

Let $A = {y : y = {log}_{2} x, x < 16, x, y \in N}, B = {x : x^{2} - 7 x + 12 = 0}$ then $(A \cup B) \times (A \cap B)$ is

{3, 3}

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

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

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

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Solution

The correct option is B ${(1, 3), (2, 3), (3, 3), (4, 3)}$
$A = {y : y = {log}_{2} x, x < 16, x, y \in N}$
for $x < 16 \Rightarrow {log}_{2} x < 4 ∴ y \in (- \infty, 4) & y \in N$
$∴ A = {1, 2, 3}$
$B = {x : x^{2} - 7 x + 12 = 0} \Rightarrow B = {3, 4}$
$A \cup B = {1, 2, 3, 4} A \cap B = {3} ∴ (A \cup B) \times (A \cap B) = {(1, 3), (2, 3), (3, 3), (4, 3)}$

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Let A={y:y=log2x,x<16,x,y∈N},B={x:x2−7x+12=0} then (A∪B)×(A∩B) is

The correct option is B {(1,3),(2,3),(3,3),(4,3)}A={y:y=log2x,x<16,x,y∈N} for x<16⇒log2x<4∴y∈(−∞,4) & y∈N ∴A={1,2,3} B={x:x2−7x+12=0}⇒B={3,4} A∪B={1,2,3,4}A∩B={3}∴(A∪B)×(A∩B)={(1,3),(2,3),(3,3),(4,3)}

Let $A = {y : y = {log}_{2} x, x < 16, x, y \in N}, B = {x : x^{2} - 7 x + 12 = 0}$ then $(A \cup B) \times (A \cap B)$ is