Two sets A and B are as under:
A = {(a, b) ∈ R × R: |a − 5|

Question

Two sets A and B are as under:
A = {(a, b) ∈ R × R: |a − 5| < 1 and |b − 5| < 1};
B = {(a, b) ∈ R × R: 4(a − 6)² + 9(b − 5)² ≤ 36}.
Then:

Accepted Answer

A ⊂ B. A is the open square 4<a<6, 4<b<6. On it, 4(a-6)^2 + 9(b-5)^2 is largest at a corner, value 4(4)+9(1)=25, which is < 36, so every point of A satisfies B. Hence A is a subset of B.

Two sets A and B are as under: A = {(a, b) ∈ R × R: |a − 5| < 1 and |b − 5| < 1}; B = {(a, b) ∈ R × R: 4(a − 6)² + 9(b − 5)² ≤ 36}. Then:

Solution

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