Let A - x - x -11- x - N - Let R be a relation on A defined by x - y - R if and only if x -2 y -10- Which of the following is false-A- Both b and c- R -2-4-4-3-6-2-8-1C- Domain of R -1-2-4-6-8D- Range of R -1-2-3-4-5

The correct option is A Both (b) and (c)As per definition of R, R={(x,y):x+2y=10, 1≤ x,y≤10, x,y∈ℕ} ⇒ R={(2,4),(4,3),(6,2),(8,1)} ∴ Options (b) and (c) are inc ...

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Byju's Answer

Standard XII

Mathematics

Cartesian Product

Let A = x : x...

Question

Let $A = {x : x < 11, x \in N}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $x + 2 y = 10$ . Which of the following is false?

R = {(2, 4), (4, 3), (6, 2), (8, 1)}

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Domain of

R = {1, 2, 4, 6, 8}

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Range of

R = {1, 2, 3, 4, 5}

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Both (b) and (c)

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Solution

The correct option is D Both (b) and (c)
As per definition of $R$ ,
$R = {(x, y) : x + 2 y = 10, 1 \leq x, y \leq 10, x, y \in N} \Rightarrow R = {(2, 4), (4, 3), (6, 2), (8, 1)}$
$∴$ Options $(b)$ and $(c)$ are incorrect.

Suggest Corrections

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Let A={x:x<11,x∈N}. Let R be a relation on A defined by (x,y)∈R if and only if x+2y=10. Which of the following is false?

The correct option is D Both (b) and (c)As per definition of R, R={(x,y):x+2y=10,1≤x,y≤10,x,y∈N}⇒R={(2,4),(4,3),(6,2),(8,1)} ∴ Options (b) and (c) are incorrect.

Let $A = {x : x < 11, x \in N}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $x + 2 y = 10$ . Which of the following is false?

The correct option is D Both (b) and (c)
As per definition of $R$ ,
$R = {(x, y) : x + 2 y = 10, 1 \leq x, y \leq 10, x, y \in N} \Rightarrow R = {(2, 4), (4, 3), (6, 2), (8, 1)}$
$∴$ Options $(b)$ and $(c)$ are incorrect.