Question

Given A = {x -1 ≤ x ≤ 5, x E R} and B = {x: -4 < x < 5, x = R} Find the range of set A n B and represent it on a number line​

Answer 1

Answer:

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Step-by-step explanation:

A ∩ B = {x: -1 < x < 3, x ∈ R} It can be represented on a number line as: (ii) Numbers which belong to B but do not belong to A = B - A A' ∩ B = {x: - 4 ≤ x ≤ -1, x ∈ R} It can be represented on a number line as: (iii) A - B = {x: 3 ≤ x ≤ 5, x ∈ R} It can be represented on a number line as: Read more on Sarthaks.com - https://www.sarthaks.com/145942/given-a-x-1-x-5-x-r-and-b-x-4-x-3-x-r-represent-on-different-number-lines-i-a-b-ii-a-b-iii-a-b

Answer 2

Answer:

Given, P={x : 5<2x−1≤11,x∈R} and Q={x : −1≤3+4x<23,x∈I}

Solving for P,

5<2x−1≤11

⇒5+1<2x≤11+1

⇒6<2x≤12

⇒3<x≤6

Hence, P={x : 3<x≤6,x∈R}

The solution P is represented on number line (a).

Next, solving for Q

−⇒1≤3+4x<23

⇒−1−3≤4x<23−3

⇒−4≤4x<20

⇒−1≤x<5

As Q∈I

Hence, solution Q={−1,0,1,2,3,4}

The solution Q is represented on number line (b).

Therefore, P∩Q={4}

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