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Two sets A and B are as under A=|(a,b) i...

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

`B sub A`

B

`A sub B`

C

`A cap B=phi`(an empty set)

D

neither ` A sub B " nor " B sub A`

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`|a-5| lt 1 and |b-5| lt 1`
`therefore -1 lt a -5 lt 1 and -1 lt b -5 lt 1`
` rArr 4 lt a lt 6 and 4 lt b lt 6`
Now, ` 4 (a-6)^(2)+9(b-5)^(2) le 36`
` rArr ((a-6)^(2))/(9)+((b-5)^(2))/(4) le 1 `
Talking axes as a-axis and b-axis

The set A represents square PQRS inside set B representing ellipse and hence `A sub B.`
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