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Two sets A and B are as under `A=|(a,b) in RxxR:|a-5| lt 1 and |b-5| lt 1} B=[(a,b) in Rxx R:4(a-6)^2+9(b-5)^2 le 36} Then:` (1) `B sub A` (2) `A sub B` (3) `AnnB =phi ( an empty set) (4) neither `A sub B` nor `B sub A`

A

neither `AsubB"nor"BsubA`

B

`BsubA`

C

`AsubB`

D

`AsubB=phi` (an empty set)

Text Solution

Verified by Experts

Let a x=a and b=y
So, we have `|x-5|lt 1 and |y-5|lt1" "(1)`
`|x-5|lt1`
`rArr-1ltx-5lt1`
`rArr4ltxlt6`
Similary, `4ltyl,t6`
Thus, we have a square for inequality (1)
Now,`4(x-6)^(2)+9(y-5)^(2)le36`
`rArr((x-6)^(2))/(9)+((y-5)^(2))/(4)le" "(2)`
Points satsfying above indquality lies inside ellipse or on the ellipse having center at (6,5).
Regios of both the inequalities are plotted as shown in the following figure :
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