If A - x - 4-3 x -2 - 13- x - R and B - x -2 - 5-7 x -40- x - I - then write down the element of A - B-4 MARKS-

Each set: 1 Mark each Calculations: 1 Mark Answer: 1 Mark 4 lt;3x 2≤ 13, x ϵ R ⇒ 6 lt;3x≤ 15 ⇒ 2 lt; x ≤ 5 ∴ A={ 3, 4, 5 } and 2 ≤ 5 +7x lt;40, x ϵ ...

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Byju's Answer

Standard X

Mathematics

Modulus Function

If A = x : 4<...

Question

If $A = {x : 4 < 3 x - 2 \leq 13, x ϵ R}$ and $B = {x : - 2 \leq 5 + 7 x < 40, x ϵ I}$ , then write down the element of $A \cap B$ .
[4 MARKS]

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Solution

Each set: 1 Mark each
Calculations: 1 Mark
Answer: 1 Mark

$4 < 3 x - 2 \leq 13, x ϵ R \Rightarrow 6 < 3 x \leq 15 \Rightarrow 2 < x \leq 5 ∴ A = {3, 4, 5} a n d - 2 \leq 5 + 7 x < 40, x ϵ I \Rightarrow - 7 \leq 7 x < 35 \Rightarrow - 1 \leq x < 5$
So, B = ${- 1, 0, 1, 2, 3. 4}$
Hence $A \cap B = {3, 4}$

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If A={x:4<3x−2≤13,x ϵ R} and B={x:−2≤5+7x<40,x ϵ I}, then write down the element of A∩B. [4 MARKS]

Each set: 1 Mark each Calculations: 1 Mark Answer: 1 Mark 4<3x−2≤13,xϵR⇒ 6<3x≤15⇒ 2<x≤5∴ A={3,4,5}and−2≤5+7x<40,xϵI⇒ −7≤7x<35⇒ −1≤x<5 So, B = {−1,0,1,2,3.4} Hence A∩B={3,4}

If $A = {x : 4 < 3 x - 2 \leq 13, x ϵ R}$ and $B = {x : - 2 \leq 5 + 7 x < 40, x ϵ I}$ , then write down the element of $A \cap B$ .
[4 MARKS]